MACHINERY''''S HANDBOOK 27th CD 2 Episode 8 pps

2834 SQUARES OF NUMBERS
To find the square of a given whole number, divide the number by 10 and find the row in the first
column that contains the whole number portion of the result. The selected row contains the square of
given number under the column corresponding to the last digit in the number.
Example:The square of 673, found in row labeled 67, under column labeled 3, is given as 452,929.
51 260100 261121 262144 263169 264196 265225 266256 267289 268324 269361
52 270400 271441 272484 273529 274576 275625 276676 277729 278784 279841
53 280900 281961 283024 284089 285156 286225 287296 288369 289444 290521
54 291600 292681 293764 294849 295936 297025 298116 299209 300304 301401
55 302500 303601 304704 305809 306916 308025 309136 310249 311364 312481
56 313600 314721 315844 316969 318096 319225 320356 321489 322624 323761
57 324900 326041 327184 328329 329476 330625 331776 332929 334084 335241
58 336400 337561 338724 339889 341056 342225 343396 344569 345744 346921
59 348100 349281 350464 351649 352836 354025 355216 356409 357604 358801
60 360000 361201 362404 363609 364816 366025 367236 368449 369664 370881
61 372100 373321 374544 375769 376996 378225 379456 380689 381924 383161
62 384400 385641 386884 388129 389376 390625 391876 393129 394384 395641
63 396900 398161 399424 400689 401956 403225 404496 405769 407044 408321
64 409600 410881 412164 413449 414736 416025 417316 418609 419904 421201
65 422500 423801 425104 426409 427716 429025 430336 431649 432964 434281
66 435600 436921 438244 439569 440896 442225 443556 444889 446224 447561
67 448900 450241 451584 452929 454276 455625 456976 458329 459684 461041
68 462400 463761 465124 466489 467856 469225 470596 471969 473344 474721
69 476100 477481 478864 480249 481636 483025 484416 485809 487204 488601
70 490000 491401 492804 494209 495616 497025 498436 499849 501264 502681
71 504100 505521 506944 508369 509796 511225 512656 514089 515524 516961
72 518400 519841 521284 522729 524176 525625 527076 528529 529984 531441
73 532900 534361 535824 537289 538756 540225 541696 543169 544644 546121
74 547600 549081 550564 552049 553536 555025 556516 558009 559504 561001
75 562500 564001 565504 567009 568516 570025 571536 573049 574564 576081

76 577600 579121 580644 582169 583696 585225 586756 588289 589824 591361
77 592900 594441 595984 597529 599076 600625 602176 603729 605284 606841
78 608400 609961 611524 613089 614656 616225 617796 619369 620944 622521
79 624100 625681 627264 628849 630436 632025 633616 635209 636804 638401
80 640000 641601 643204 644809 646416 648025 649636 651249 652864 654481
81 656100 657721 659344 660969 662596 664225 665856 667489 669124 670761
82 672400 674041 675684 677329 678976 680625 682276 683929 685584 687241
83 688900 690561 692224 693889 695556 697225 698896 700569 702244 703921
84 705600 707281 708964 710649 712336 714025 715716 717409 719104 720801
85 722500 724201 725904 727609 729316 731025 732736 734449 736164 737881
86 739600 741321 743044 744769 746496 748225 749956 751689 753424 755161
87 756900 758641 760384 762129 763876 765625 767376 769129 770884 772641
88 774400 776161 777924 779689 781456 783225 784996 786769 788544 790321
89 792100 793881 795664 797449 799236 801025 802816 804609 806404 808201
90 810000 811801 813604 815409 817216 819025 820836 822649 824464 826281
91 828100 829921 831744 833569 835396 837225 839056 840889 842724 844561
92 846400 848241 850084 851929 853776 855625 857476 859329 861184 863041
93 864900 866761 868624 870489 872356 874225 876096 877969 879844 881721
94 883600 885481 887364 889249 891136 893025 894916 896809 898704 900601
95 902500 904401 906304 908209 910116 912025 913936 915849 917764 919681
96 921600 923521 925444 927369 929296 931225 933156 935089 937024 938961
97 940900 942841 944784 946729 948676 950625 952576 954529 956484 958441
98 960400 962361 964324 966289 968256 970225 972196 974169 976144 978121
99 980100 982081 984064 986049 988036 990025 992016 994009 996004 998001
Squares of Numbers from 1 to 999
0123456789
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SQUARES OF MIXED NUMBERS 2835
Squares of Mixed Numbers from

1
⁄
64
to 6, by 64ths
No.012345

1
⁄
64
0.00024 1.03149 4.06274 9.09399 16.12524 25.15649

1
⁄
32
0.00098 1.06348 4.12598 9.18848 16.25098 25.31348

3
⁄
64
0.00220 1.09595 4.18970 9.28345 16.37720 25.47095

1
⁄
16
0.00391 1.12891 4.25391 9.37891 16.50391 25.62891

5
⁄
64
0.00610 1.16235 4.31860 9.47485 16.63110 25.78735

3
⁄
32
0.00879 1.19629 4.38379 9.57129 16.75879 25.94629

7
⁄
64
0.01196 1.23071 4.44946 9.66821 16.88696 26.10571

1
⁄
8
0.01563 1.26563 4.51563 9.76563 17.01563 26.26563

9
⁄
64
0.01978 1.30103 4.58228 9.86353 17.14478 26.42603

5
⁄
32
0.02441 1.33691 4.64941 9.96191 17.27441 26.58691

11
⁄
64
0.02954 1.37329 4.71704 10.06079 17.40454 26.74829

3
⁄
16
0.03516 1.41016 4.78516 10.16016 17.53516 26.91016

13
⁄
64
0.04126 1.44751 4.85376 10.26001 17.66626 27.07251

7
⁄
32
0.04785 1.48535 4.92285 10.36035 17.79785 27.23535

15
⁄
64
0.05493 1.52368 4.99243 10.46118 17.92993 27.39868

1
⁄
4
0.06250 1.56250 5.06250 10.56250 18.06250 27.56250

17
⁄
64
0.07056 1.60181 5.13306 10.66431 18.19556 27.72681

9
⁄
32
0.07910 1.64160 5.20410 10.76660 18.32910 27.89160

19
⁄
64
0.08813 1.68188 5.27563 10.86938 18.46313 28.05688

5
⁄
16
0.09766 1.72266 5.34766 10.97266 18.59766 28.22266

21
⁄
64
0.10767 1.76392 5.42017 11.07642 18.73267 28.38892

11
⁄
32
0.11816 1.80566 5.49316 11.18066 18.86816 28.55566

23
⁄
64
0.12915 1.84790 5.56665 11.28540 19.00415 28.72290

3
⁄
8
0.14063 1.89063 5.64063 11.39063 19.14063 28.89063

25
⁄
64
0.15259 1.93384 5.71509 11.49634 19.27759 29.05884

13
⁄
32
0.16504 1.97754 5.79004 11.60254 19.41504 29.22754

27
⁄
64
0.17798 2.02173 5.86548 11.70923 19.55298 29.39673

7
⁄
16
0.19141 2.06641 5.94141 11.81641 19.69141 29.56641

29
⁄
64
0.20532 2.11157 6.01782 11.92407 19.83032 29.73657

15
⁄
32
0.21973 2.15723 6.09473 12.03223 19.96973 29.90723

31
⁄
64
0.23462 2.20337 6.17212 12.14087 20.10962 30.07837

1
⁄
2
0.25000 2.25000 6.25000 12.25000 20.25000 30.25000

33
⁄
64
0.26587 2.29712 6.32837 12.35962 20.39087 30.42212

17
⁄
32
0.28223 2.34473 6.40723 12.46973 20.53223 30.59473

35
⁄
64
0.29907 2.39282 6.48657 12.58032 20.67407 30.76782

9
⁄
16
0.31641 2.44141 6.56641 12.69141 20.81641 30.94141

37
⁄
64
0.33423 2.49048 6.64673 12.80298 20.95923 31.11548

19
⁄
32
0.35254 2.54004 6.72754 12.91504 21.10254 31.29004

39
⁄
64
0.37134 2.59009 6.80884 13.02759 21.24634 31.46509

5
⁄
8
0.39063 2.64063 6.89063 13.14063 21.39063 31.64063

41
⁄
64
0.41040 2.69165 6.97290 13.25415 21.53540 31.81665

21
⁄
32
0.43066 2.74316 7.05566 13.36816 21.68066 31.99316

43
⁄
64
0.45142 2.79517 7.13892 13.48267 21.82642 32.17017

11
⁄
16
0.47266 2.84766 7.22266 13.59766 21.97266 32.34766

45
⁄
64
0.49438 2.90063 7.30688 13.71313 22.11938 32.52563

23
⁄
32
0.51660 2.95410 7.39160 13.82910 22.26660 32.70410

47
⁄
64
0.53931 3.00806 7.47681 13.94556 22.41431 32.88306

3
⁄
4
0.56250 3.06250 7.56250 14.06250 22.56250 33.06250

49
⁄
64
0.58618 3.11743 7.64868 14.17993 22.71118 33.24243

25
⁄
32
0.61035 3.17285 7.73535 14.29785 22.86035 33.42285

51
⁄
64
0.63501 3.22876 7.82251 14.41626 23.01001 33.60376

13
⁄
16
0.66016 3.28516 7.91016 14.53516 23.16016 33.78516

53
⁄
64
0.68579 3.34204 7.99829 14.65454 23.31079 33.96704

27
⁄
32
0.71191 3.39941 8.08691 14.77441 23.46191 34.14941

55
⁄
64
0.73853 3.45728 8.17603 14.89478 23.61353 34.33228

7
⁄
8
0.76563 3.51563 8.26563 15.01563 23.76563 34.51563

57
⁄
64
0.79321 3.57446 8.35571 15.13696 23.91821 34.69946

29
⁄
32
0.82129 3.63379 8.44629 15.25879 24.07129 34.88379

59
⁄
64
0.84985 3.69360 8.53735 15.38110 24.22485 35.06860

15
⁄
16
0.87891 3.75391 8.62891 15.50391 24.37891 35.25391

61
⁄
64
0.90845 3.81470 8.72095 15.62720 24.53345 35.43970

31
⁄
32
0.93848 3.87598 8.81348 15.75098 24.68848 35.62598

63
⁄
64
0.96899 3.93774 8.90649 15.87524 24.84399 35.81274
1 1.00000 4.00000 9.00000 16.00000 25.00000 36.00000
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2836 SQUARES OF MIXED NUMBERS
Squares of Mixed Numbers from 6
1
⁄
64
to 12, by 64ths
No.67891011

1
⁄
64
36.18774 49.21899 64.25024 81.28149 100.31274 121.34399

1
⁄
32
36.37598 49.43848 64.50098 81.56348 100.62598 121.68848

3
⁄
64
36.56470 49.65845 64.75220 81.84595 100.93970 122.03345

1
⁄
16
36.75391 49.87891 65.00391 82.12891 101.25391 122.37891

5
⁄
64
36.94360 50.09985 65.25610 82.41235 101.56860 122.72485

3
⁄
32
37.13379 50.32129 65.50879 82.69629 101.88379 123.07129

7
⁄
64
37.32446 50.54321 65.76196 82.98071 102.19946 123.41821

1
⁄
8
37.51563 50.76563 66.01563 83.26563 102.51563 123.76563

9
⁄
64
37.70728 50.98853 66.26978 83.55103 102.83228 124.11353

5
⁄
32
37.89941 51.21191 66.52441 83.83691 103.14941 124.46191

11
⁄
64
38.09204 51.43579 66.77954 84.12329 103.46704 124.81079

3
⁄
16
38.28516 51.66016 67.03516 84.41016 103.78516 125.16016

13
⁄
64
38.47876 51.88501 67.29126 84.69751 104.10376 125.51001

7
⁄
32
38.67285 52.11035 67.54785 84.98535 104.42285 125.86035

15
⁄
64
38.86743 52.33618 67.80493 85.27368 104.74243 126.21118

1
⁄
4
39.06250 52.56250 68.06250 85.56250 105.06250 126.56250

17
⁄
64
39.25806 52.78931 68.32056 85.85181 105.38306 126.91431

9
⁄
32
39.45410 53.01660 68.57910 86.14160 105.70410 127.26660

19
⁄
64
39.65063 53.24438 68.83813 86.43188 106.02563 127.61938

5
⁄
16
39.84766 53.47266 69.09766 86.72266 106.34766 127.97266

21
⁄
64
40.04517 53.70142 69.35767 87.01392 106.67017 128.32642

11
⁄
32
40.24316 53.93066 69.61816 87.30566 106.99316 128.68066

23
⁄
64
40.44165 54.16040 69.87915 87.59790 107.31665 129.03540

3
⁄
8
40.64063 54.39063 70.14063 87.89063 107.64063 129.39063

25
⁄
64
40.84009 54.62134 70.40259 88.18384 107.96509 129.74634

13
⁄
32
41.04004 54.85254 70.66504 88.47754 108.29004 130.10254

27
⁄
64
41.24048 55.08423 70.92798 88.77173 108.61548 130.45923

7
⁄
16
41.44141 55.31641 71.19141 89.06641 108.94141 130.81641

29
⁄
64
41.64282 55.54907 71.45532 89.36157 109.26782 131.17407

15
⁄
32
41.84473 55.78223 71.71973 89.65723 109.59473 131.53223

31
⁄
64
42.04712 56.01587 71.98462 89.95337 109.92212 131.89087

1
⁄
2
42.25000 56.25000 72.25000 90.25000 110.25000 132.25000

33
⁄
64
42.45337 56.48462 72.51587 90.54712 110.57837 132.60962

17
⁄
32
42.65723 56.71973 72.78223 90.84473 110.90723 132.96973

35
⁄
64
42.86157 56.95532 73.04907 91.14282 111.23657 133.33032

9
⁄
16
43.06641 57.19141 73.31641 91.44141 111.56641 133.69141

37
⁄
64
43.27173 57.42798 73.58423 91.74048 111.89673 134.05298

19
⁄
32
43.47754 57.66504 73.85254 92.04004 112.22754 134.41504

39
⁄
64
43.68384 57.90259 74.12134 92.34009 112.55884 134.77759

5
⁄
8
43.89063 58.14063 74.39063 92.64063 112.89063 135.14063

41
⁄
64
44.09790 58.37915 74.66040 92.94165 113.22290 135.50415

21
⁄
32
44.30566 58.61816 74.93066 93.24316 113.55566 135.86816

43
⁄
64
44.51392 58.85767 75.20142 93.54517 113.88892 136.23267

11
⁄
16
44.72266 59.09766 75.47266 93.84766 114.22266 136.59766

45
⁄
64
44.93188 59.33813 75.74438 94.15063 114.55688 136.96313

23
⁄
32
45.14160 59.57910 76.01660 94.45410 114.89160 137.32910

47
⁄
64
45.35181 59.82056 76.28931 94.75806 115.22681 137.69556

3
⁄
4
45.56250 60.06250 76.56250 95.06250 115.56250 138.06250

49
⁄
64
45.77368 60.30493 76.83618 95.36743 115.89868 138.42993

25
⁄
32
45.98535 60.54785 77.11035 95.67285 116.23535 138.79785

51
⁄
64
46.19751 60.79126 77.38501 95.97876 116.57251 139.16626

13
⁄
16
46.41016 61.03516 77.66016 96.28516 116.91016 139.53516

53
⁄
64
46.62329 61.27954 77.93579 96.59204 117.24829 139.90454

27
⁄
32
46.83691 61.52441 78.21191 96.89941 117.58691 140.27441

55
⁄
64
47.05103 61.76978 78.48853 97.20728 117.92603 140.64478

7
⁄
8
47.26563 62.01563 78.76563 97.51563 118.26563 141.01563

57
⁄
64
47.48071 62.26196 79.04321 97.82446 118.60571 141.38696

29
⁄
32
47.69629 62.50879 79.32129 98.13379 118.94629 141.75879

59
⁄
64
47.91235 62.75610 79.59985 98.44360 119.28735 142.13110

15
⁄
16
48.12891 63.00391 79.87891 98.75391 119.62891 142.50391

61
⁄
64
48.34595 63.25220 80.15845 99.06470 119.97095 142.87720

31
⁄
32
48.56348 63.50098 80.43848 99.37598 120.31348 143.25098

63
⁄
64
48.78149 63.75024 80.71899 99.68774 120.65649 143.62524
1 49.00000 64.00000 81.00000 100.00000 121.00000 144.00000
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SQUARES AND CUBES OF NUMBERS 2837
Squares and Cubes of Fractions
Squares and Cubes of Numbers from
1
⁄
32
to 6
15
⁄
16
No. Square Cube No. Square Cube No. Square Cube

1
⁄
32
0.00098 0.00003
1
17
⁄
32
2.34473 3.59036 4 16.00000 64.00000

1
⁄
16
0.00391 0.00024
1
9
⁄
16
2.44141 3.81470
4
1
⁄
16
16.50391 67.04712

3
⁄
32
0.00879 0.00082
1

19
⁄
32
2.54004 4.04819
4
1
⁄
8
17.01563 70.18945

1
⁄
8
0.01563 0.00195
1
5
⁄
8
2.64063 4.29102
4
3
⁄
16
17.53516 73.42847

5
⁄
32
0.02441 0.00381
1

21
⁄
32
2.74316 4.54337
4
1
⁄
4
18.06250 76.76563

3
⁄
16
0.03516 0.00659
1
11
⁄
16
2.84766 4.80542
4
5
⁄
16
18.59766 80.20239

7
⁄
32
0.04785 0.01047
1

23
⁄
32
2.95410 5.07736
4
3
⁄
8
19.14063 83.74023

1
⁄
4
0.06250 0.01563
1
3
⁄
4
3.06250 5.35938
4
7
⁄
16
19.69141 87.38062

9
⁄
32
0.07910 0.02225
1

25
⁄
32
3.17285 5.65164
4
1
⁄
2
20.25000 91.12500

5
⁄
16
0.09766 0.03052
1
13
⁄
16
3.28516 5.95435
4
9
⁄
16
20.81641 94.97485

11
⁄
32
0.11816 0.04062
1

27
⁄
32
3.39941 6.26767
4
5
⁄
8
21.39063 98.93164

3
⁄
8
0.14063 0.05273
1
7
⁄
8
3.51563 6.59180
4
11
⁄
16
21.97266 102.99683

13
⁄
32
0.16504 0.06705
1

29
⁄
32
3.63379 6.92691
4
3
⁄
4
22.56250 107.17188

7
⁄
16
0.19141 0.08374
1
15
⁄
16
3.75391 7.27319
4
13
⁄
16
23.16016 111.45825

15
⁄
32
0.21973 0.10300
1

31
⁄
32
3.87598 7.63083
4
7
⁄
8
23.76563 115.85742

1
⁄
2
0.25000 0.12500 2 4.00000 8.00000
4
15
⁄
16
24.37891 120.37085

17
⁄
32
0.28223 0.14993
2
1
⁄
32
4.12598 8.38089 5 25.00000 125.00000

9
⁄
16
0.31641 0.17798
2
1
⁄
16
4.25391 8.77368
5
1
⁄
16
25.62891 129.74634

19
⁄
32
0.35254 0.20932
2
1
⁄
8
4.51563 9.59570
5
1
⁄
8
26.26563 134.61133

5
⁄
8
0.39063 0.24414
2
3
⁄
16
4.78516 10.46753
5
3
⁄
16
26.91016 139.59644

21
⁄
32
0.43066 0.28262
2
1
⁄
4
5.06250 11.39063
5
1
⁄
4
27.56250 144.70313

11
⁄
16
0.47266 0.32495
2
5
⁄
16
5.34766 12.36646
5
5
⁄
16
28.22266 149.93286

23
⁄
32
0.51660 0.37131
2
3
⁄
8
5.64063 13.39648
5
3
⁄
8
28.89063 155.28711

3
⁄
4
0.56250 0.42188
2
7
⁄
16
5.94141 14.48218
5
7
⁄
16
29.56641 160.76733

25
⁄
32
0.61035 0.47684
2
1
⁄
2
6.25000 15.62500
5
1
⁄
2
30.25000 166.37500

13
⁄
16
0.66016 0.53638
2
9
⁄
16
6.56641 16.82642
5
9
⁄
16
30.94141 172.11157

27
⁄
32
0.71191 0.60068
2
5
⁄
8
6.89063 18.08789
5
5
⁄
8
31.64063 177.97852

7
⁄
8
0.76563 0.66992
2
11
⁄
16
7.22266 19.41089
5
11
⁄
16
32.34766 183.97729

29
⁄
32
0.82129 0.74429
2
3
⁄
4
7.56250 20.79688
5
3
⁄
4
33.06250 190.10938

15
⁄
16
0.87891 0.82397
2
13
⁄
16
7.91016 22.24731
5
13
⁄
16
33.78516 196.37622

31
⁄
32
0.93848 0.90915
2
7
⁄
8
8.26563 23.76367
5
7
⁄
8
34.51563 202.77930
1 1.00000 1.00000

2
15
⁄
16
8.62891 25.34741
5
15
⁄
16
35.25391 209.32007
1
1
⁄
32
1.06348 1.09671 3 9.00000 27.00000 6 36.00000 216.00000
1
1
⁄
16
1.12891 1.19946
3
1
⁄
16
9.37891 28.72290
6
1
⁄
16
36.75391 222.82056

1
3
⁄
32
1.19629 1.30844
3
1
⁄
8
9.76563 30.51758
6
1
⁄
8
37.51563 229.78320
1
1
⁄
8
1.26563 1.42383
3
3
⁄
16
10.16016 32.38550
6
3
⁄
16
38.28516 236.88940

1
5
⁄
32
1.33691 1.54581
3
1
⁄
4
10.56250 34.32813
6
1
⁄
4
39.06250 244.14063
1
3
⁄
16
1.41016 1.67456
3
5
⁄
16
10.97266 36.34692
6
5
⁄
16
39.84766 251.53833

1
7
⁄
32
1.48535 1.81027
3
3
⁄
8
11.39063 38.44336
6
3
⁄
8
40.64063 259.08398
1
1
⁄
4
1.56250 1.95313
3
7
⁄
16
11.81641 40.61890
6
7
⁄
16
41.44141 266.77905

1
9
⁄
32
1.64160 2.10330
3
1
⁄
2
12.25000 42.87500
6
1
⁄
2
42.25000 274.62500
1
5
⁄
16
1.72266 2.26099
3
9
⁄
16
12.69141 45.21313
6
9
⁄
16
43.06641 282.62329

1
11
⁄
32
1.80566 2.42636
3
5
⁄
8
13.14063 47.63477
6
5
⁄
8
43.89063 290.77539
1
3
⁄
8
1.89063 2.59961
3
11
⁄
16
13.59766 50.14136
6
11
⁄
16
44.72266 299.08276

1
13
⁄
32
1.97754 2.78091
3
3
⁄
4
14.06250 52.73438
6
3
⁄
4
45.56250 307.54688
1
7
⁄
16
2.06641 2.97046
3
13
⁄
16
14.53516 55.41528
6
13
⁄
16
46.41016 316.16919

1
15
⁄
32
2.15723 3.16843
3
7
⁄
8
15.01563 58.18555
6
7
⁄
8
47.26563 324.95117
1
1
⁄
2
2.25000 3.37500
3
15
⁄
16
15.50391 61.04663
6
15
⁄
16
48.12891 333.89429

Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2838 SQUARES AND CUBES OF NUMBERS
Squares and Cubes of Numbers from 7 to 21
7
⁄
8
No. Square Cube No. Square Cube No. Square Cube
7 49.00000 343.00000 10 100.00000 1000.00000 16 256.00000 4096.00000

1
⁄
16
49.87891 352.26978

1
⁄
8
102.51563 1037.97070

1
⁄
8
260.01563 4192.75195

1
⁄
8
50.76563 361.70508

1
⁄
4
105.06250 1076.89063

1
⁄
4
264.06250 4291.01563

3
⁄
16
51.66016 371.30737

3
⁄
8
107.64063 1116.77148

3
⁄
8
268.14063 4390.80273

1
⁄
4
52.56250 381.07813

1
⁄
2
110.25000 1157.62500

1
⁄
2
272.25000 4492.12500

5
⁄
16
53.47266 391.01880

5
⁄
8
112.89063 1199.46289

5
⁄
8
276.39063 4594.99414

3
⁄
8
54.39063 401.13086

3
⁄
4
115.56250 1242.29688

3
⁄
4
280.56250 4699.42188

7
⁄
16
55.31641 411.41577

7
⁄
8
118.26563 1286.13867

7
⁄
8
284.76563 4805.41992

1
⁄
2
56.25000 421.87500 11 121.00000 1331.00000 17 289.00000 4913.00000

9
⁄
16
57.19141 432.51001

1
⁄
8
123.76563 1376.89258

1
⁄
8
293.26563 5022.17383

5
⁄
8
58.14063 443.32227

1
⁄
4
126.56250 1423.82813

1
⁄
4
297.56250 5132.95313

11
⁄
16
59.09766 454.31323

3
⁄
8
129.39063 1471.81836

3
⁄
8
301.89063 5245.34961

3
⁄
4
60.06250 465.48438

1
⁄
2
132.25000 1520.87500

1
⁄
2
306.25000 5359.37500

13
⁄
16
61.03516 476.83716

5
⁄
8
135.14063 1571.00977

5
⁄
8
310.64063 5475.04102

7
⁄
8
62.01563 488.37305

3
⁄
4
138.06250 1622.23438

3
⁄
4
315.06250 5592.35938

15
⁄
16
63.00391 500.09351

7
⁄
8
141.01563 1674.56055

7
⁄
8
319.51563 5711.34180
8 64.00000 512.00000 12 144.00000 1728.00000 18 324.00000 5832.00000

1
⁄
16
65.00391 524.09399

1
⁄
8
147.01563 1782.56445

1
⁄
8
328.51563 5954.34570

1
⁄
8
66.01563 536.37695

1
⁄
4
150.06250 1838.26563

1
⁄
4
333.06250 6078.39063

3
⁄
16
67.03516 548.85034

3
⁄
8
153.14063 1895.11523

3
⁄
8
337.64063 6204.14648

1
⁄
4
68.06250 561.51563

1
⁄
2
156.25000 1953.12500

1
⁄
2
342.25000 6331.62500

5
⁄
16
69.09766 574.37427

5
⁄
8
159.39063 2012.30664

5
⁄
8
346.89063 6460.83789

3
⁄
8
70.14063 587.42773

3
⁄
4
162.56250 2072.67188

3
⁄
4
351.56250 6591.79688

7
⁄
16
71.19141 600.67749

7
⁄
8
165.76563 2134.23242

7
⁄
8
356.26563 6724.51367

1
⁄
2
72.25000 614.12500 13 169.00000 2197.00000 19 361.00000 6859.00000

9
⁄
16
73.31641 627.77173

1
⁄
8
172.26563 2260.98633

1
⁄
8
365.76563 6995.26758

5
⁄
8
74.39063 641.61914

1
⁄
4
175.56250 2326.20313

1
⁄
4
370.56250 7133.32813

11
⁄
16
75.47266 655.66870

3
⁄
8
178.89063 2392.66211

3
⁄
8
375.39063 7273.19336

3
⁄
4
76.56250 669.92188

1
⁄
2
182.25000 2460.37500

1
⁄
2
380.25000 7414.87500

13
⁄
16
77.66016 684.38013

5
⁄
8
185.64063 2529.35352

5
⁄
8
385.14063 7558.38477

7
⁄
8
78.76563 699.04492

3
⁄
4
189.06250 2599.60938

3
⁄
4
390.06250 7703.73438

15
⁄
16
79.87891 713.91772

7
⁄
8
192.51563 2671.15430

7
⁄
8
395.01563 7850.93555
9 81.00000 729.00000 14 196.00000 2744.00000 20 400.00000 8000.00000

1
⁄
16
82.12891 744.29321

1
⁄
8

199.51563 2818.15820

1
⁄
8
405.01563 8150.93945

1
⁄
8
83.26563 759.79883

1
⁄
4
203.06250 2893.64063

1
⁄
4
410.06250 8303.76563

3
⁄
16
84.41016 775.51831

3
⁄
8

206.64063 2970.45898

3
⁄
8
415.14063 8458.49023

1
⁄
4
85.56250 791.45313

1
⁄
2
210.25000 3048.62500

1
⁄
2
420.25000 8615.12500

5
⁄
16
86.72266 807.60474

5
⁄
8

213.89063 3128.15039

5
⁄
8
425.39063 8773.68164

3
⁄
8
87.89063 823.97461

3
⁄
4
217.56250 3209.04688

3
⁄
4
430.56250 8934.17188

7
⁄
16
89.06641 840.56421

7
⁄
8

221.26563 3291.32617

7
⁄
8
435.76563 9096.60742

1
⁄
2
90.25000 857.37500 15 225.00000 3375.00000 21 441.00000 9261.00000

9
⁄
16
91.44141 874.40845

1
⁄
8
228.76563 3460.08008

1
⁄
8
446.26563 9427.36133

5
⁄
8

92.64063 891.66602

1
⁄
4
232.56250 3546.57813

1
⁄
4
451.56250 9595.70313

11
⁄
16
93.84766 909.14917

3
⁄
8
236.39063 3634.50586

3
⁄
8
456.89063 9766.03711

3
⁄
4

95.06250 926.85938

1
⁄
2
240.25000 3723.87500

1
⁄
2
462.25000 9938.37500

13
⁄
16
96.28516 944.79810

5
⁄
8
244.14063 3814.69727

5
⁄
8
467.64063 10112.72852

7
⁄
8

97.51563 962.96680

3
⁄
4
248.06250 3906.98438

3
⁄
4
473.06250 10289.10938

15
⁄
16
98.75391 981.36694

7
⁄
8
252.01563 4000.74805

7
⁄
8
478.51563 10467.52930
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SQUARES AND CUBES OF NUMBERS 2839
Squares and Cubes of Numbers from 22 to 39

7
⁄
8
No. Square Cube No. Square Cube No. Square Cube
22 484.00000 10648.00000 28 784.00000 21952.00000 34 1156.00000 39304.00000

1
⁄
8
489.51563 10830.53320

1
⁄
8
791.01563 22247.31445

1
⁄
8
1164.51563 39739.09570

1
⁄
4
495.06250 11015.14063

1
⁄
4
798.06250 22545.26563

1
⁄
4
1173.06250 40177.39063

3
⁄
8
500.64063 11201.83398

3
⁄
8
805.14063 22845.86523

3
⁄
8
1181.64063 40618.89648

1
⁄
2
506.25000 11390.62500

1
⁄
2
812.25000 23149.12500

1
⁄
2
1190.25000 41063.62500

5
⁄
8
511.89063 11581.52539

5
⁄
8
819.39063 23455.05664

5
⁄
8
1198.89063 41511.58789

3
⁄
4
517.56250 11774.54688

3
⁄
4
826.56250 23763.67188

3
⁄
4
1207.56250 41962.79688

7
⁄
8
523.26563 11969.70117

7
⁄
8
833.76563 24074.98242

7
⁄
8
1216.26563 42417.26367
23 529.00000 12167.00000 29 841.00000 24389.00000 35 1225.00000 42875.00000

1
⁄
8
534.76563 12366.45508

1
⁄
8

848.26563 24705.73633

1
⁄
8
1233.76563 43336.01758

1
⁄
4
540.56250 12568.07813

1
⁄
4
855.56250 25025.20313

1
⁄
4
1242.56250 43800.32813

3
⁄
8
546.39063 12771.88086

3
⁄
8

862.89063 25347.41211

3
⁄
8
1251.39063 44267.94336

1
⁄
2
552.25000 12977.87500

1
⁄
2
870.25000 25672.37500

1
⁄
2
1260.25000 44738.87500

5
⁄
8
558.14063 13186.07227

5
⁄
8

877.64063 26000.10352

5
⁄
8
1269.14063 45213.13477

3
⁄
4
564.06250 13396.48438

3
⁄
4
885.06250 26330.60938

3
⁄
4
1278.06250 45690.73438

7
⁄
8
570.01563 13609.12305

7
⁄
8

892.51563 26663.90430

7
⁄
8
1287.01563 46171.68555
24 576.00000 13824.00000 30 900.00000 27000.00000 36 1296.00000 46656.00000

1
⁄
8
582.01563 14041.12695

1
⁄
8
907.51563 27338.90820

1
⁄
8
1305.01563 47143.68945

1
⁄
4
588.06250 14260.51563

1
⁄

4
915.06250 27680.64063

1
⁄
4
1314.06250 47634.76563

3
⁄
8
594.14063 14482.17773

3
⁄
8
922.64063 28025.20898

3
⁄
8
1323.14063 48129.24023

1
⁄
2
600.25000 14706.12500

1
⁄

2
930.25000 28372.62500

1
⁄
2
1332.25000 48627.12500

5
⁄
8
606.39063 14932.36914

5
⁄
8
937.89063 28722.90039

5
⁄
8
1341.39063 49128.43164

3
⁄
4
612.56250 15160.92188

3
⁄

4
945.56250 29076.04688

3
⁄
4
1350.56250 49633.17188

7
⁄
8
618.76563 15391.79492

7
⁄
8
953.26563 29432.07617

7
⁄
8
1359.76563 50141.35742
25 625.00000 15625.00000 31 961.00000 29791.00000 37 1369.00000 50653.00000

1
⁄
8
631.26563 15860.54883

1

⁄
8
968.76563 30152.83008

1
⁄
8
1378.26563 51168.11133

1
⁄
4
637.56250 16098.45313

1
⁄
4
976.56250 30517.57813

1
⁄
4
1387.56250 51686.70313

3
⁄
8
643.89063 16338.72461

3

⁄
8
984.39063 30885.25586

3
⁄
8
1396.89063 52208.78711

1
⁄
2
650.25000 16581.37500

1
⁄
2
992.25000 31255.87500

1
⁄
2
1406.25000 52734.37500

5
⁄
8
656.64063 16826.41602

5

⁄
8
1000.14063 31629.44727

5
⁄
8
1415.64063 53263.47852

3
⁄
4
663.06250 17073.85938

3
⁄
4
1008.06250 32005.98438

3
⁄
4
1425.06250 53796.10938

7
⁄
8
669.51563 17323.71680

7

⁄
8
1016.01563 32385.49805

7
⁄
8
1434.51563 54332.27930
26 676.00000 17576.00000 32 1024.00000 32768.00000 38 1444.00000 54872.00000

1
⁄
8
682.51563 17830.72070

1
⁄
8
1032.01563 33153.50195

1
⁄
8
1453.51563 55415.28320

1
⁄
4
689.06250 18087.89063

1
⁄
4
1040.06250 33542.01563

1
⁄
4
1463.06250 55962.14063

3
⁄
8
695.64063 18347.52148

3
⁄
8
1048.14063 33933.55273

3
⁄
8
1472.64063 56512.58398

1
⁄
2
702.25000 18609.62500

1
⁄
2
1056.25000 34328.12500

1
⁄
2
1482.25000 57066.62500

5
⁄
8
708.89063 18874.21289

5
⁄
8
1064.39063 34725.74414

5
⁄
8
1491.89063 57624.27539

3
⁄
4
715.56250 19141.29688

3
⁄
4
1072.56250 35126.42188

3
⁄
4
1501.56250 58185.54688

7
⁄
8
722.26563 19410.88867

7
⁄
8
1080.76563 35530.16992

7
⁄
8
1511.26563 58750.45117
27 729.00000 19683.00000 33 1089.00000 35937.00000 39 1521.00000 59319.00000

1
⁄
8
735.76563 19957.64258

1
⁄
8
1097.26563 36346.92383

1
⁄
8
1530.76563 59891.20508

1
⁄
4
742.56250 20234.82813

1
⁄
4
1105.56250 36759.95313

1
⁄
4
1540.56250 60467.07813

3
⁄
8
749.39063 20514.56836

3
⁄
8
1113.89063 37176.09961

3
⁄
8
1550.39063 61046.63086

1
⁄
2
756.25000 20796.87500

1
⁄
2
1122.25000 37595.37500

1
⁄
2
1560.25000 61629.87500

5
⁄
8
763.14063 21081.75977

5
⁄
8
1130.64063 38017.79102

5
⁄
8
1570.14063 62216.82227

3
⁄
4
770.06250 21369.23438

3
⁄
4
1139.06250 38443.35938

3
⁄
4
1580.06250 62807.48438

7
⁄
8
777.01563 21659.31055

7
⁄
8
1147.51563 38872.09180

7
⁄
8
1590.01563 63401.87305
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2840 SQUARES AND CUBES OF NUMBERS
Squares and Cubes of Numbers from 40 to 57
7
⁄
8
No. Square Cube No. Square Cube No. Square Cube
40 1600.00000 64000.00000 46 2116.00000 97336.00000 52 2704.00000 140608.00000

1
⁄
8
1610.01563 64601.87695

1
⁄
8
2127.51563 98131.65820

1
⁄
8
2717.01563 141624.43945

1
⁄
4
1620.06250 65207.51563

1
⁄
4
2139.06250 98931.64063

1
⁄
4
2730.06250 142645.76563

3
⁄
8
1630.14063 65816.92773

3
⁄
8
2150.64063 99735.95898

3
⁄
8
2743.14063 143671.99023

1
⁄
2
1640.25000 66430.12500

1
⁄
2
2162.25000 100544.62500

1
⁄
2
2756.25000 144703.12500

5
⁄
8
1650.39063 67047.11914

5
⁄
8
2173.89063 101357.65039

5
⁄
8
2769.39063 145739.18164

3
⁄
4
1660.56250 67667.92188

3
⁄
4
2185.56250 102175.04688

3
⁄
4
2782.56250 146780.17188

7
⁄
8
1670.76563 68292.54492

7
⁄
8
2197.26563 102996.82617

7
⁄
8
2795.76563 147826.10742
41 1681.00000 68921.00000 47 2209.00000 103823.00000 53 2809.00000 148877.00000

1
⁄
8
1691.26563 69553.29883

1
⁄
8
2220.76563 104653.58008

1
⁄
8
2822.26563 149932.86133

1
⁄
4
1701.56250 70189.45313

1
⁄
4
2232.56250 105488.57813

1
⁄
4
2835.56250 150993.70313

3
⁄
8
1711.89063 70829.47461

3
⁄
8
2244.39063 106328.00586

3
⁄
8
2848.89063 152059.53711

1
⁄
2
1722.25000 71473.37500

1
⁄
2
2256.25000 107171.87500

1
⁄
2
2862.25000 153130.37500

5
⁄
8
1732.64063 72121.16602

5
⁄
8
2268.14063 108020.19727

5
⁄
8
2875.64063 154206.22852

3
⁄
4
1743.06250 72772.85938

3
⁄
4
2280.06250 108872.98438

3
⁄
4
2889.06250 155287.10938

7
⁄
8
1753.51563 73428.46680

7
⁄
8
2292.01563 109730.24805

7
⁄
8
2902.51563 156373.02930
42 1764.00000 74088.00000 48 2304.00000 110592.00000 54 2916.00000 157464.00000

1
⁄
8
1774.51563 74751.47070

1
⁄
8

2316.01563 111458.25195

1
⁄
8
2929.51563 158560.03320

1
⁄
4
1785.06250 75418.89063

1
⁄
4
2328.06250 112329.01563

1
⁄
4
2943.06250 159661.14063

3
⁄
8
1795.64063 76090.27148

3
⁄
8

2340.14063 113204.30273

3
⁄
8
2956.64063 160767.33398

1
⁄
2
1806.25000 76765.62500

1
⁄
2
2352.25000 114084.12500

1
⁄
2
2970.25000 161878.62500

5
⁄
8
1816.89063 77444.96289

5
⁄
8

2364.39063 114968.49414

5
⁄
8
2983.89063 162995.02539

3
⁄
4
1827.56250 78128.29688

3
⁄
4
2376.56250 115857.42188

3
⁄
4
2997.56250 164116.54688

7
⁄
8
1838.26563 78815.63867

7
⁄
8

2388.76563 116750.91992

7
⁄
8
3011.26563 165243.20117
43 1849.00000 79507.00000 49 2401.00000 117649.00000 55 3025.00000 166375.00000

1
⁄
8
1859.76563 80202.39258

1
⁄
8
2413.26563 118551.67383

1
⁄
8
3038.76563 167511.95508

1
⁄
4
1870.56250 80901.82813

1
⁄

4
2425.56250 119458.95313

1
⁄
4
3052.56250 168654.07813

3
⁄
8
1881.39063 81605.31836

3
⁄
8
2437.89063 120370.84961

3
⁄
8
3066.39063 169801.38086

1
⁄
2
1892.25000 82312.87500

1
⁄

2
2450.25000 121287.37500

1
⁄
2
3080.25000 170953.87500

5
⁄
8
1903.14063 83024.50977

5
⁄
8
2462.64063 122208.54102

5
⁄
8
3094.14063 172111.57227

3
⁄
4
1914.06250 83740.23438

3
⁄

4
2475.06250 123134.35938

3
⁄
4
3108.06250 173274.48438

7
⁄
8
1925.01563 84460.06055

7
⁄
8
2487.51563 124064.84180

7
⁄
8
3122.01563 174442.62305
44 1936.00000 85184.00000 50 2500.00000 125000.00000 56 3136.00000 175616.00000

1
⁄
8
1947.01563 85912.06445

1

⁄
8
2512.51563 125939.84570

1
⁄
8
3150.01563 176794.62695

1
⁄
4
1958.06250 86644.26563

1
⁄
4
2525.06250 126884.39063

1
⁄
4
3164.06250 177978.51563

3
⁄
8
1969.14063 87380.61523

3

⁄
8
2537.64063 127833.64648

3
⁄
8
3178.14063 179167.67773

1
⁄
2
1980.25000 88121.12500

1
⁄
2
2550.25000 128787.62500

1
⁄
2
3192.25000 180362.12500

5
⁄
8
1991.39063 88865.80664

5

⁄
8
2562.89063 129746.33789

5
⁄
8
3206.39063 181561.86914

3
⁄
4
2002.56250 89614.67188

3
⁄
4
2575.56250 130709.79688

3
⁄
4
3220.56250 182766.92188

7
⁄
8
2013.76563 90367.73242

7

⁄
8
2588.26563 131678.01367

7
⁄
8
3234.76563 183977.29492
45 2025.00000 91125.00000 51 2601.00000 132651.00000 57 3249.00000 185193.00000

1
⁄
8
2036.26563 91886.48633

1
⁄
8
2613.76563 133628.76758

1
⁄
8
3263.26563 186414.04883

1
⁄
4
2047.56250 92652.20313

1
⁄
4
2626.56250 134611.32813

1
⁄
4
3277.56250 187640.45313

3
⁄
8
2058.89063 93422.16211

3
⁄
8
2639.39063 135598.69336

3
⁄
8
3291.89063 188872.22461

1
⁄
2
2070.25000 94196.37500

1
⁄
2
2652.25000 136590.87500

1
⁄
2
3306.25000 190109.37500

5
⁄
8
2081.64063 94974.85352

5
⁄
8
2665.14063 137587.88477

5
⁄
8
3320.64063 191351.91602

3
⁄
4
2093.06250 95757.60938

3
⁄
4
2678.06250 138589.73438

3
⁄
4
3335.06250 192599.85938

7
⁄
8
2104.51563 96544.65430

7
⁄
8
2691.01563 139596.43555

7
⁄
8
3349.51563 193853.21680
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SQUARES AND CUBES OF NUMBERS 2841
Squares and Cubes of Numbers from 58 to 75
7
⁄

8
No. Square Cube No. Square Cube No. Square Cube
58 3364.00000 195112.00000 64 4096.00000 262144.00000 70 4900.00000 343000.00000

1
⁄
8
3378.51563 196376.22070

1
⁄
8
4112.01563 263683.00195

1
⁄
8
4917.51563 344840.78320

1
⁄
4
3393.06250 197645.89063

1
⁄
4
4128.06250 265228.01563

1

⁄
4
4935.06250 346688.14063

3
⁄
8
3407.64063 198921.02148

3
⁄
8
4144.14063 266779.05273

3
⁄
8
4952.64063 348542.08398

1
⁄
2
3422.25000 200201.62500

1
⁄
2
4160.25000 268336.12500

1

⁄
2
4970.25000 350402.62500

5
⁄
8
3436.89063 201487.71289

5
⁄
8
4176.39063 269899.24414

5
⁄
8
4987.89063 352269.77539

3
⁄
4
3451.56250 202779.29688

3
⁄
4
4192.56250 271468.42188

3

⁄
4
5005.56250 354143.54688

7
⁄
8
3466.26563 204076.38867

7
⁄
8
4208.76563 273043.66992

7
⁄
8
5023.26563 356023.95117
59 3481.00000 205379.00000 65 4225.00000 274625.00000 71 5041.00000 357911.00000

1
⁄
8
3495.76563 206687.14258

1
⁄
8
4241.26563 276212.42383

1
⁄
8
5058.76563 359804.70508

1
⁄
4
3510.56250 208000.82813

1
⁄
4
4257.56250 277805.95313

1
⁄
4
5076.56250 361705.07813

3
⁄
8
3525.39063 209320.06836

3
⁄
8
4273.89063 279405.59961

3
⁄
8
5094.39063 363612.13086

1
⁄
2
3540.25000 210644.87500

1
⁄
2
4290.25000 281011.37500

1
⁄
2
5112.25000 365525.87500

5
⁄
8
3555.14063 211975.25977

5
⁄
8
4306.64063 282623.29102

5
⁄
8
5130.14063 367446.32227

3
⁄
4
3570.06250 213311.23438

3
⁄
4
4323.06250 284241.35938

3
⁄
4
5148.06250 369373.48438

7
⁄
8
3585.01563 214652.81055

7
⁄
8
4339.51563 285865.59180

7
⁄
8
5166.01563 371307.37305
60 3600.00000 216000.00000 66 4356.00000 287496.00000 72 5184.00000 373248.00000

1
⁄
8
3615.01563 217352.81445

1
⁄
8
4372.51563 289132.59570

1
⁄
8
5202.01563 375195.37695

1
⁄
4
3630.06250 218711.26563

1
⁄
4
4389.06250 290775.39063

1
⁄
4
5220.06250 377149.51563

3
⁄
8
3645.14063 220075.36523

3
⁄
8
4405.64063 292424.39648

3
⁄
8
5238.14063 379110.42773

1
⁄
2
3660.25000 221445.12500

1
⁄
2
4422.25000 294079.62500

1
⁄
2
5256.25000 381078.12500

5
⁄
8
3675.39063 222820.55664

5
⁄
8
4438.89063 295741.08789

5
⁄
8
5274.39063 383052.61914

3
⁄
4
3690.56250 224201.67188

3
⁄
4
4455.56250 297408.79688

3
⁄
4
5292.56250 385033.92188

7
⁄
8
3705.76563 225588.48242

7
⁄
8
4472.26563 299082.76367

7
⁄
8
5310.76563 387022.04492
61 3721.00000 226981.00000 67 4489.00000 300763.00000 73 5329.00000 389017.00000

1
⁄
8
3736.26563 228379.23633

1
⁄
8

4505.76563 302449.51758

1
⁄
8
5347.26563 391018.79883

1
⁄
4
3751.56250 229783.20313

1
⁄
4
4522.56250 304142.32813

1
⁄
4
5365.56250 393027.45313

3
⁄
8
3766.89063 231192.91211

3
⁄
8

4539.39063 305841.44336

3
⁄
8
5383.89063 395042.97461

1
⁄
2
3782.25000 232608.37500

1
⁄
2
4556.25000 307546.87500

1
⁄
2
5402.25000 397065.37500

5
⁄
8
3797.64063 234029.60352

5
⁄
8

4573.14063 309258.63477

5
⁄
8
5420.64063 399094.66602

3
⁄
4
3813.06250 235456.60938

3
⁄
4
4590.06250 310976.73438

3
⁄
4
5439.06250 401130.85938

7
⁄
8
3828.51563 236889.40430

7
⁄
8

4607.01563 312701.18555

7
⁄
8
5457.51563 403173.96680
62 3844.00000 238328.00000 68 4624.00000 314432.00000 74 5476.00000 405224.00000

1
⁄
8
3859.51563 239772.40820

1
⁄
8
4641.01563 316169.18945

1
⁄
8
5494.51563 407280.97070

1
⁄
4
3875.06250 241222.64063

1
⁄

4
4658.06250 317912.76563

1
⁄
4
5513.06250 409344.89063

3
⁄
8
3890.64063 242678.70898

3
⁄
8
4675.14063 319662.74023

3
⁄
8
5531.64063 411415.77148

1
⁄
2
3906.25000 244140.62500

1
⁄

2
4692.25000 321419.12500

1
⁄
2
5550.25000 413493.62500

5
⁄
8
3921.89063 245608.40039

5
⁄
8
4709.39063 323181.93164

5
⁄
8
5568.89063 415578.46289

3
⁄
4
3937.56250 247082.04688

3
⁄

4
4726.56250 324951.17188

3
⁄
4
5587.56250 417670.29688

7
⁄
8
3953.26563 248561.57617

7
⁄
8
4743.76563 326726.85742

7
⁄
8
5606.26563 419769.13867
63 3969.00000 250047.00000 69 4761.00000 328509.00000 75 5625.00000 421875.00000

1
⁄
8
3984.76563 251538.33008

1

⁄
8
4778.26563 330297.61133

1
⁄
8
5643.76563 423987.89258

1
⁄
4
4000.56250 253035.57813

1
⁄
4
4795.56250 332092.70313

1
⁄
4
5662.56250 426107.82813

3
⁄
8
4016.39063 254538.75586

3

⁄
8
4812.89063 333894.28711

3
⁄
8
5681.39063 428234.81836

1
⁄
2
4032.25000 256047.87500

1
⁄
2
4830.25000 335702.37500

1
⁄
2
5700.25000 430368.87500

5
⁄
8
4048.14063 257562.94727

5

⁄
8
4847.64063 337516.97852

5
⁄
8
5719.14063 432510.00977

3
⁄
4
4064.06250 259083.98438

3
⁄
4
4865.06250 339338.10938

3
⁄
4
5738.06250 434658.23438

7
⁄
8
4080.01563 260610.99805

7

⁄
8
4882.51563 341165.77930

7
⁄
8
5757.01563 436813.56055
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2842 SQUARES AND CUBES OF NUMBERS
Squares and Cubes of Numbers from 76 to 93
7
⁄
8
No. Square Cube No. Square Cube No. Square Cube
76 5776.00000 438976.00000 82 6724.00000 551368.00000 88 7744.00000 681472.00000

1
⁄
8
5795.01563 441145.56445

1
⁄
8
6744.51563 553893.34570

1
⁄

8
7766.01563 684380.12695

1
⁄
4
5814.06250 443322.26563

1
⁄
4
6765.06250 556426.39063

1
⁄
4
7788.06250 687296.51563

3
⁄
8
5833.14063 445506.11523

3
⁄
8
6785.64063 558967.14648

3
⁄

8
7810.14063 690221.17773

1
⁄
2
5852.25000 447697.12500

1
⁄
2
6806.25000 561515.62500

1
⁄
2
7832.25000 693154.12500

5
⁄
8
5871.39063 449895.30664

5
⁄
8
6826.89063 564071.83789

5
⁄

8
7854.39063 696095.36914

3
⁄
4
5890.56250 452100.67188

3
⁄
4
6847.56250 566635.79688

3
⁄
4
7876.56250 699044.92188

7
⁄
8
5909.76563 454313.23242

7
⁄
8
6868.26563 569207.51367

7
⁄

8
7898.76563 702002.79492
77 5929.00000 456533.00000 83 6889.00000 571787.00000 89 7921.00000 704969.00000

1
⁄
8
5948.26563 458759.98633

1
⁄
8
6909.76563 574374.26758

1
⁄
8
7943.26563 707943.54883

1
⁄
4
5967.56250 460994.20313

1
⁄
4
6930.56250 576969.32813

1

⁄
4
7965.56250 710926.45313

3
⁄
8
5986.89063 463235.66211

3
⁄
8
6951.39063 579572.19336

3
⁄
8
7987.89063 713917.72461

1
⁄
2
6006.25000 465484.37500

1
⁄
2
6972.25000 582182.87500

1

⁄
2
8010.25000 716917.37500

5
⁄
8
6025.64063 467740.35352

5
⁄
8
6993.14063 584801.38477

5
⁄
8
8032.64063 719925.41602

3
⁄
4
6045.06250 470003.60938

3
⁄
4
7014.06250 587427.73438

3

⁄
4
8055.06250 722941.85938

7
⁄
8
6064.51563 472274.15430

7
⁄
8
7035.01563 590061.93555

7
⁄
8
8077.51563 725966.71680
78 6084.00000 474552.00000 84 7056.00000 592704.00000 90 8100.00000 729000.00000

1
⁄
8
6103.51563 476837.15820

1
⁄
8
7077.01563 595353.93945

1
⁄
8
8122.51563 732041.72070

1
⁄
4
6123.06250 479129.64063

1
⁄
4
7098.06250 598011.76563

1
⁄
4
8145.06250 735091.89063

3
⁄
8
6142.64063 481429.45898

3
⁄
8
7119.14063 600677.49023

3
⁄
8
8167.64063 738150.52148

1
⁄
2
6162.25000 483736.62500

1
⁄
2
7140.25000 603351.12500

1
⁄
2
8190.25000 741217.62500

5
⁄
8
6181.89063 486051.15039

5
⁄
8
7161.39063 606032.68164

5
⁄
8
8212.89063 744293.21289

3
⁄
4
6201.56250 488373.04688

3
⁄
4
7182.56250 608722.17188

3
⁄
4
8235.56250 747377.29688

7
⁄
8
6221.26563 490702.32617

7
⁄
8
7203.76563 611419.60742

7
⁄
8
8258.26563 750469.88867
79 6241.00000 493039.00000 85 7225.00000 614125.00000 91 8281.00000 753571.00000

1
⁄
8
6260.76563 495383.08008

1
⁄
8
7246.26563 616838.36133

1
⁄
8
8303.76563 756680.64258

1
⁄
4
6280.56250 497734.57813

1
⁄
4
7267.56250 619559.70313

1
⁄
4
8326.56250 759798.82813

3
⁄
8
6300.39063 500093.50586

3
⁄
8
7288.89063 622289.03711

3
⁄
8
8349.39063 762925.56836

1
⁄
2
6320.25000 502459.87500

1
⁄
2
7310.25000 625026.37500

1
⁄
2
8372.25000 766060.87500

5
⁄
8
6340.14063 504833.69727

5
⁄
8
7331.64063 627771.72852

5
⁄
8
8395.14063 769204.75977

3
⁄
4
6360.06250 507214.98438

3
⁄
4
7353.06250 630525.10938

3
⁄
4
8418.06250 772357.23438

7
⁄
8
6380.01563 509603.74805

7
⁄
8
7374.51563 633286.52930

7
⁄
8
8441.01563 775518.31055
80 6400.00000 512000.00000 86 7396.00000 636056.00000 92 8464.00000 778688.00000

1
⁄
8
6420.01563 514403.75195

1
⁄
8

7417.51563 638833.53320

1
⁄
8
8487.01563 781866.31445

1
⁄
4
6440.06250 516815.01563

1
⁄
4
7439.06250 641619.14063

1
⁄
4
8510.06250 785053.26563

3
⁄
8
6460.14063 519233.80273

3
⁄
8

7460.64063 644412.83398

3
⁄
8
8533.14063 788248.86523

1
⁄
2
6480.25000 521660.12500

1
⁄
2
7482.25000 647214.62500

1
⁄
2
8556.25000 791453.12500

5
⁄
8
6500.39063 524093.99414

5
⁄
8

7503.89063 650024.52539

5
⁄
8
8579.39063 794666.05664

3
⁄
4
6520.56250 526535.42188

3
⁄
4
7525.56250 652842.54688

3
⁄
4
8602.56250 797887.67188

7
⁄
8
6540.76563 528984.41992

7
⁄
8

7547.26563 655668.70117

7
⁄
8
8625.76563 801117.98242
81 6561.00000 531441.00000 87 7569.00000 658503.00000 93 8649.00000 804357.00000

1
⁄
8
6581.26563 533905.17383

1
⁄
8
7590.76563 661345.45508

1
⁄
8
8672.26563 807604.73633

1
⁄
4
6601.56250 536376.95313

1
⁄

4
7612.56250 664196.07813

1
⁄
4
8695.56250 810861.20313

3
⁄
8
6621.89063 538856.34961

3
⁄
8
7634.39063 667054.88086

3
⁄
8
8718.89063 814126.41211

1
⁄
2
6642.25000 541343.37500

1
⁄

2
7656.25000 669921.87500

1
⁄
2
8742.25000 817400.37500

5
⁄
8
6662.64063 543838.04102

5
⁄
8
7678.14063 672797.07227

5
⁄
8
8765.64063 820683.10352

3
⁄
4
6683.06250 546340.35938

3
⁄

4
7700.06250 675680.48438

3
⁄
4
8789.06250 823974.60938

7
⁄
8
6703.51563 548850.34180

7
⁄
8
7722.01563 678572.12305

7
⁄
8
8812.51563 827274.90430
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
FRACTIONS OF PI 2843
Squares and Cubes of Numbers from 94 to 100
Fractions of Pi (π)
Table of Fractions of π = 3.14159265
No. Square Cube No. Square Cube No. Square Cube
94 8836.00000 830584.00000 96 9216.00000 884736.00000 98 9604.00000 941192.00000

1
⁄
8
8859.51563 833901.90820

1
⁄
8
9240.01563 888196.50195

1
⁄
8
9628.51563 944798.09570

1
⁄
4
8883.06250 837228.64063

1
⁄
4
9264.06250 891666.01563

1
⁄
4
9653.06250 948413.39063

3
⁄
8
8906.64063 840564.20898

3
⁄
8
9288.14063 895144.55273

3
⁄
8
9677.64063 952037.89648

1
⁄
2
8930.25000 843908.62500

1
⁄
2
9312.25000 898632.12500

1
⁄
2
9702.25000 955671.62500

5
⁄
8
8953.89063 847261.90039

5
⁄
8
9336.39063 902128.74414

5
⁄
8
9726.89063 959314.58789

3
⁄
4
8977.56250 850624.04688

3
⁄
4
9360.56250 905634.42188

3
⁄
4
9751.56250 962966.79688

7
⁄
8
9001.26563 853995.07617

7
⁄
8
9384.76563 909149.16992

7
⁄
8
9776.26563 966628.26367
95 9025.00000 857375.00000 97 9409.00000 912673.00000 99 9801.00000 970299.00000

1
⁄
8
9048.76563 860763.83008

1
⁄
8
9433.26563 916205.92383

1
⁄
8

9825.76563 973979.01758

1
⁄
4
9072.56250 864161.57813

1
⁄
4
9457.56250 919747.95313

1
⁄
4
9850.56250 977668.32813

3
⁄
8
9096.39063 867568.25586

3
⁄
8
9481.89063 923299.09961

3
⁄
8

9875.39063 981366.94336

1
⁄
2
9120.25000 870983.87500

1
⁄
2
9506.25000 926859.37500

1
⁄
2
9900.25000 985074.87500

5
⁄
8
9144.14063 874408.44727

5
⁄
8
9530.64063 930428.79102

5
⁄
8

9925.14063 988792.13477

3
⁄
4
9168.06250 877841.98438

3
⁄
4
9555.06250 934007.35938

3
⁄
4
9950.06250 992518.73438

7
⁄
8
9192.01563 881284.49805

7
⁄
8
9579.51563 937595.09180

7
⁄
8

9975.01563 996254.68555
100 10,000.00 1,000,000
a π/a a π/a a π/a a π/a a π/a
1 3.14159 21 0.14960 41 0.07662 61 0.05150 81 0.03879
2 1.57080 22 0.14280 42 0.07480 62 0.05067 82 0.03831
3 1.04720 23 0.13659 43 0.07306 63 0.04987 83 0.03785
4 0.78540 24 0.13090 44 0.07140 64 0.04909 84 0.03740
5 0.62832 25 0.12566 45 0.06981 65 0.04833 85 0.03696
6 0.52360 26 0.12083 46 0.06830 66 0.04760 86 0.03653
7 0.44880 27 0.11636 47 0.06684 67 0.04689 87 0.03611
8 0.39270 28 0.11220 48 0.06545 68 0.04620 88 0.03570
9 0.34907 29 0.10833 49 0.06411 69 0.04553 89 0.03530
10 0.31416 30 0.10472 50 0.06283 70 0.04488 90 0.03491
11 0.28560 31 0.10134 51 0.06160 71 0.04425 91 0.03452
12 0.26180 32 0.09817 52 0.06042 72 0.04363 92 0.03415
13 0.24166 33 0.09520 53 0.05928 73 0.04304 93 0.03378
14 0.22440 34 0.09240 54 0.05818 74 0.04245 94 0.03342
15 0.20944 35 0.08976 55 0.05712 75 0.04189 95 0.03307
16 0.19635 36 0.08727 56 0.05610 76 0.04134 96 0.03272
17 0.18480 37 0.08491 57 0.05512 77 0.04080 97 0.03239
18 0.17453 38 0.08267 58 0.05417 78 0.04028 98 0.03206
19 0.16535 39 0.08055 59 0.05325 79 0.03977 99 0.03173
20 0.15708 40 0.07854 60 0.05236 80 0.03927 100 0.03142
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2844 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals
Powers, Roots, and Reciprocals From 1 to 50
No. Square Cube Sq. Root Cube Root Reciprocal No.
1 1 1 1.00000 1.00000 1.0000000 1

2 4 8 1.41421 1.25992 0.5000000 2
3 9 27 1.73205 1.44225 0.3333333 3
4 16 64 2.00000 1.58740 0.2500000 4
5 25 125 2.23607 1.70998 0.2000000 5
6 36 216 2.44949 1.81712 0.1666667 6
7 49 343 2.64575 1.91293 0.1428571 7
8 64 512 2.82843 2.00000 0.1250000 8
9 81 729 3.00000 2.08008 0.1111111 9
10 100 1000 3.16228 2.15443 0.1000000 10
11 121 1331 3.31662 2.22398 0.0909091 11
12 144 1728 3.46410 2.28943 0.0833333 12
13 169 2197 3.60555 2.35133 0.0769231 13
14 196 2744 3.74166 2.41014 0.0714286 14
15 225 3375 3.87298 2.46621 0.0666667 15
16 256 4096 4.00000 2.51984 0.0625000 16
17 289 4913 4.12311 2.57128 0.0588235 17
18 324 5832 4.24264 2.62074 0.0555556 18
19 361 6859 4.35890 2.66840 0.0526316 19
20 400 8000 4.47214 2.71442 0.0500000 20
21 441 9261 4.58258 2.75892 0.0476190 21
22 484 10648 4.69042 2.80204 0.0454545 22
23 529 12167 4.79583 2.84387 0.0434783 23
24 576 13824 4.89898 2.88450 0.0416667 24
25 625 15625 5.00000 2.92402 0.0400000 25
26 676 17576 5.09902 2.96250 0.0384615 26
27 729 19683 5.19615 3.00000 0.0370370 27
28 784 21952 5.29150 3.03659 0.0357143 28
29 841 24389 5.38516 3.07232 0.0344828 29
30 900 27000 5.47723 3.10723 0.0333333 30
31 961 29791 5.56776 3.14138 0.0322581 31

32 1024 32768 5.65685 3.17480 0.0312500 32
33 1089 35937 5.74456 3.20753 0.0303030 33
34 1156 39304 5.83095 3.23961 0.0294118 34
35 1225 42875 5.91608 3.27107 0.0285714 35
36 1296 46656 6.00000 3.30193 0.0277778 36
37 1369 50653 6.08276 3.33222 0.0270270 37
38 1444 54872 6.16441 3.36198 0.0263158 38
39 1521 59319 6.24500 3.39121 0.0256410 39
40 1600 64000 6.32456 3.41995 0.0250000 40
41 1681 68921 6.40312 3.44822 0.0243902 41
42 1764 74088 6.48074 3.47603 0.0238095 42
43 1849 79507 6.55744 3.50340 0.0232558 43
44 1936 85184 6.63325 3.53035 0.0227273 44
45 2025 91125 6.70820 3.55689 0.0222222 45
46 2116 97336 6.78233 3.58305 0.0217391 46
47 2209 103823 6.85565 3.60883 0.0212766 47
48 2304 110592 6.92820 3.63424 0.0208333 48
49 2401 117649 7.00000 3.65931 0.0204082 49
50 2500 125000 7.07107 3.68403 0.0200000 50
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2845
Powers, Roots, and Reciprocals From 51 to 100
No. Square Cube Sq. Root Cube Root Reciprocal No.
51 2601 132651 7.14143 3.70843 0.0196078 51
52 2704 140608 7.21110 3.73251 0.0192308 52
53 2809 148877 7.28011 3.75629 0.0188679 53
54 2916 157464 7.34847 3.77976 0.0185185 54
55 3025 166375 7.41620 3.80295 0.0181818 55
56 3136 175616 7.48331 3.82586 0.0178571 56

57 3249 185193 7.54983 3.84850 0.0175439 57
58 3364 195112 7.61577 3.87088 0.0172414 58
59 3481 205379 7.68115 3.89300 0.0169492 59
60 3600 216000 7.74597 3.91487 0.0166667 60
61 3721 226981 7.81025 3.93650 0.0163934 61
62 3844 238328 7.87401 3.95789 0.0161290 62
63 3969 250047 7.93725 3.97906 0.0158730 63
64 4096 262144 8.00000 4.00000 0.0156250 64
65 4225 274625 8.06226 4.02073 0.0153846 65
66 4356 287496 8.12404 4.04124 0.0151515 66
67 4489 300763 8.18535 4.06155 0.0149254 67
68 4624 314432 8.24621 4.08166 0.0147059 68
69 4761 328509 8.30662 4.10157 0.0144928 69
70 4900 343000 8.36660 4.12129 0.0142857 70
71 5041 357911 8.42615 4.14082 0.0140845 71
72 5184 373248 8.48528 4.16017 0.0138889 72
73 5329 389017 8.54400 4.17934 0.0136986 73
74 5476 405224 8.60233 4.19834 0.0135135 74
75 5625 421875 8.66025 4.21716 0.0133333 75
76 5776 438976 8.71780 4.23582 0.0131579 76
77 5929 456533 8.77496 4.25432 0.0129870 77
78 6084 474552 8.83176 4.27266 0.0128205 78
79 6241 493039 8.88819 4.29084 0.0126582 79
80 6400 512000 8.94427 4.30887 0.0125000 80
81 6561 531441 9.00000 4.32675 0.0123457 81
82 6724 551368 9.05539 4.34448 0.0121951 82
83 6889 571787 9.11043 4.36207 0.0120482 83
84 7056 592704 9.16515 4.37952 0.0119048 84
85 7225 614125 9.21954 4.39683 0.0117647 85
86 7396 636056 9.27362 4.41400 0.0116279 86

87 7569 658503 9.32738 4.43105 0.0114943 87
88 7744 681472 9.38083 4.44796 0.0113636 88
89 7921 704969 9.43398 4.46475 0.0112360 89
90 8100 729000 9.48683 4.48140 0.0111111 90
91 8281 753571 9.53939 4.49794 0.0109890 91
92 8464 778688 9.59166 4.51436 0.0108696 92
93 8649 804357 9.64365 4.53065 0.0107527 93
94 8836 830584 9.69536 4.54684 0.0106383 94
95 9025 857375 9.74679 4.56290 0.0105263 95
96 9216 884736 9.79796 4.57886 0.0104167 96
97 9409 912673 9.84886 4.59470 0.0103093 97
98 9604 941192 9.89949 4.61044 0.0102041 98
99 9801 970299 9.94987 4.62607 0.0101010 99
100 10000 1000000 10.00000 4.64159 0.0100000 100
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2846 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 101 to 150
No. Square Cube Sq. Root Cube Root Reciprocal No.
101 10201 1030301 10.04988 4.65701 0.0099010 101
102 10404 1061208 10.09950 4.67233 0.0098039 102
103 10609 1092727 10.14889 4.68755 0.0097087 103
104 10816 1124864 10.19804 4.70267 0.0096154 104
105 11025 1157625 10.24695 4.71769 0.0095238 105
106 11236 1191016 10.29563 4.73262 0.0094340 106
107 11449 1225043 10.34408 4.74746 0.0093458 107
108 11664 1259712 10.39230 4.76220 0.0092593 108
109 11881 1295029 10.44031 4.77686 0.0091743 109
110 12100 1331000 10.48809 4.79142 0.0090909 110
111 12321 1367631 10.53565 4.80590 0.0090090 111

112 12544 1404928 10.58301 4.82028 0.0089286 112
113 12769 1442897 10.63015 4.83459 0.0088496 113
114 12996 1481544 10.67708 4.84881 0.0087719 114
115 13225 1520875 10.72381 4.86294 0.0086957 115
116 13456 1560896 10.77033 4.87700 0.0086207 116
117 13689 1601613 10.81665 4.89097 0.0085470 117
118 13924 1643032 10.86278 4.90487 0.0084746 118
119 14161 1685159 10.90871 4.91868 0.0084034 119
120 14400 1728000 10.95445 4.93242 0.0083333 120
121 14641 1771561 11.00000 4.94609 0.0082645 121
122 14884 1815848 11.04536 4.95968 0.0081967 122
123 15129 1860867 11.09054 4.97319 0.0081301 123
124 15376 1906624 11.13553 4.98663 0.0080645 124
125 15625 1953125 11.18034 5.00000 0.0080000 125
126 15876 2000376 11.22497 5.01330 0.0079365 126
127 16129 2048383 11.26943 5.02653 0.0078740 127
128 16384 2097152 11.31371 5.03968 0.0078125 128
129 16641 2146689 11.35782 5.05277 0.0077519 129
130 16900 2197000 11.40175 5.06580 0.0076923 130
131 17161 2248091 11.44552 5.07875 0.0076336 131
132 17424 2299968 11.48913 5.09164 0.0075758 132
133 17689 2352637 11.53256 5.10447 0.0075188 133
134 17956 2406104 11.57584 5.11723 0.0074627 134
135 18225 2460375 11.61895 5.12993 0.0074074 135
136 18496 2515456 11.66190 5.14256 0.0073529 136
137 18769 2571353 11.70470 5.15514 0.0072993 137
138 19044 2628072 11.74734 5.16765 0.0072464 138
139 19321 2685619 11.78983 5.18010 0.0071942 139
140 19600 2744000 11.83216 5.19249 0.0071429 140
141 19881 2803221 11.87434 5.20483 0.0070922 141

142 20164 2863288 11.91638 5.21710 0.0070423 142
143 20449 2924207 11.95826 5.22932 0.0069930 143
144 20736 2985984 12.00000 5.24148 0.0069444 144
145 21025 3048625 12.04159 5.25359 0.0068966 145
146 21316 3112136 12.08305 5.26564 0.0068493 146
147 21609 3176523 12.12436 5.27763 0.0068027 147
148 21904 3241792 12.16553 5.28957 0.0067568 148
149 22201 3307949 12.20656 5.30146 0.0067114 149
150 22500 3375000 12.24745 5.31329 0.0066667 150
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2847
Powers, Roots, and Reciprocals From 151 to 200
No. Square Cube Sq. Root Cube Root Reciprocal No.
151 22801 3442951 12.28821 5.32507 0.0066225 151
152 23104 3511808 12.32883 5.33680 0.0065789 152
153 23409 3581577 12.36932 5.34848 0.0065359 153
154 23716 3652264 12.40967 5.36011 0.0064935 154
155 24025 3723875 12.44990 5.37169 0.0064516 155
156 24336 3796416 12.49000 5.38321 0.0064103 156
157 24649 3869893 12.52996 5.39469 0.0063694 157
158 24964 3944312 12.56981 5.40612 0.0063291 158
159 25281 4019679 12.60952 5.41750 0.0062893 159
160 25600 4096000 12.64911 5.42884 0.0062500 160
161 25921 4173281 12.68858 5.44012 0.0062112 161
162 26244 4251528 12.72792 5.45136 0.0061728 162
163 26569 4330747 12.76715 5.46256 0.0061350 163
164 26896 4410944 12.80625 5.47370 0.0060976 164
165 27225 4492125 12.84523 5.48481 0.0060606 165
166 27556 4574296 12.88410 5.49586 0.0060241 166

167 27889 4657463 12.92285 5.50688 0.0059880 167
168 28224 4741632 12.96148 5.51785 0.0059524 168
169 28561 4826809 13.00000 5.52877 0.0059172 169
170 28900 4913000 13.03840 5.53966 0.0058824 170
171 29241 5000211 13.07670 5.55050 0.0058480 171
172 29584 5088448 13.11488 5.56130 0.0058140 172
173 29929 5177717 13.15295 5.57205 0.0057803 173
174 30276 5268024 13.19091 5.58277 0.0057471 174
175 30625 5359375 13.22876 5.59344 0.0057143 175
176 30976 5451776 13.26650 5.60408 0.0056818 176
177 31329 5545233 13.30413 5.61467 0.0056497 177
178 31684 5639752 13.34166 5.62523 0.0056180 178
179 32041 5735339 13.37909 5.63574 0.0055866 179
180 32400 5832000 13.41641 5.64622 0.0055556 180
181 32761 5929741 13.45362 5.65665 0.0055249 181
182 33124 6028568 13.49074 5.66705 0.0054945 182
183 33489 6128487 13.52775 5.67741 0.0054645 183
184 33856 6229504 13.56466 5.68773 0.0054348 184
185 34225 6331625 13.60147 5.69802 0.0054054 185
186 34596 6434856 13.63818 5.70827 0.0053763 186
187 34969 6539203 13.67479 5.71848 0.0053476 187
188 35344 6644672 13.71131 5.72865 0.0053191 188
189 35721 6751269 13.74773 5.73879 0.0052910 189
190 36100 6859000 13.78405 5.74890 0.0052632 190
191 36481 6967871 13.82027 5.75897 0.0052356 191
192 36864 7077888 13.85641 5.76900 0.0052083 192
193 37249 7189057 13.89244 5.77900 0.0051813 193
194 37636 7301384 13.92839 5.78896 0.0051546 194
195 38025 7414875 13.96424 5.79889 0.0051282 195
196 38416 7529536 14.00000 5.80879 0.0051020 196

197 38809 7645373 14.03567 5.81865 0.0050761 197
198 39204 7762392 14.07125 5.82848 0.0050505 198
199 39601 7880599 14.10674 5.83827 0.0050251 199
200 40000 8000000 14.14214 5.84804 0.0050000 200
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2848 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 201 to 250
No. Square Cube Sq. Root Cube Root Reciprocal No.
201 40401 8120601 14.17745 5.85777 0.0049751 201
202 40804 8242408 14.21267 5.86746 0.0049505 202
203 41209 8365427 14.24781 5.87713 0.0049261 203
204 41616 8489664 14.28286 5.88677 0.0049020 204
205 42025 8615125 14.31782 5.89637 0.0048780 205
206 42436 8741816 14.35270 5.90594 0.0048544 206
207 42849 8869743 14.38749 5.91548 0.0048309 207
208 43264 8998912 14.42221 5.92499 0.0048077 208
209 43681 9129329 14.45683 5.93447 0.0047847 209
210 44100 9261000 14.49138 5.94392 0.0047619 210
211 44521 9393931 14.52584 5.95334 0.0047393 211
212 44944 9528128 14.56022 5.96273 0.0047170 212
213 45369 9663597 14.59452 5.97209 0.0046948 213
214 45796 9800344 14.62874 5.98142 0.0046729 214
215 46225 9938375 14.66288 5.99073 0.0046512 215
216 46656 10077696 14.69694 6.00000 0.0046296 216
217 47089 10218313 14.73092 6.00925 0.0046083 217
218 47524 10360232 14.76482 6.01846 0.0045872 218
219 47961 10503459 14.79865 6.02765 0.0045662 219
220 48400 10648000 14.83240 6.03681 0.0045455 220
221 48841 10793861 14.86607 6.04594 0.0045249 221

222 49284 10941048 14.89966 6.05505 0.0045045 222
223 49729 11089567 14.93318 6.06413 0.0044843 223
224 50176 11239424 14.96663 6.07318 0.0044643 224
225 50625 11390625 15.00000 6.08220 0.0044444 225
226 51076 11543176 15.03330 6.09120 0.0044248 226
227 51529 11697083 15.06652 6.10017 0.0044053 227
228 51984 11852352 15.09967 6.10911 0.0043860 228
229 52441 12008989 15.13275 6.11803 0.0043668 229
230 52900 12167000 15.16575 6.12693 0.0043478 230
231 53361 12326391 15.19868 6.13579 0.0043290 231
232 53824 12487168 15.23155 6.14463 0.0043103 232
233 54289 12649337 15.26434 6.15345 0.0042918 233
234 54756 12812904 15.29706 6.16224 0.0042735 234
235 55225 12977875 15.32971 6.17101 0.0042553 235
236 55696 13144256 15.36229 6.17975 0.0042373 236
237 56169 13312053 15.39480 6.18846 0.0042194 237
238 56644 13481272 15.42725 6.19715 0.0042017 238
239 57121 13651919 15.45962 6.20582 0.0041841 239
240 57600 13824000 15.49193 6.21447 0.0041667 240
241 58081 13997521 15.52417 6.22308 0.0041494 241
242 58564 14172488 15.55635 6.23168 0.0041322 242
243 59049 14348907 15.58846 6.24025 0.0041152 243
244 59536 14526784 15.62050 6.24880 0.0040984 244
245 60025 14706125 15.65248 6.25732 0.0040816 245
246 60516 14886936 15.68439 6.26583 0.0040650 246
247 61009 15069223 15.71623 6.27431 0.0040486 247
248 61504 15252992 15.74802 6.28276 0.0040323 248
249 62001 15438249 15.77973 6.29119 0.0040161 249
250 62500 15625000 15.81139 6.29961 0.0040000 250
Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2849
Powers, Roots, and Reciprocals From 251 to 300
No. Square Cube Sq. Root Cube Root Reciprocal No.
251 63001 15813251 15.84298 6.30799 0.0039841 251
252 63504 16003008 15.87451 6.31636 0.0039683 252
253 64009 16194277 15.90597 6.32470 0.0039526 253
254 64516 16387064 15.93738 6.33303 0.0039370 254
255 65025 16581375 15.96872 6.34133 0.0039216 255
256 65536 16777216 16.00000 6.34960 0.0039063 256
257 66049 16974593 16.03122 6.35786 0.0038911 257
258 66564 17173512 16.06238 6.36610 0.0038760 258
259 67081 17373979 16.09348 6.37431 0.0038610 259
260 67600 17576000 16.12452 6.38250 0.0038462 260
261 68121 17779581 16.15549 6.39068 0.0038314 261
262 68644 17984728 16.18641 6.39883 0.0038168 262
263 69169 18191447 16.21727 6.40696 0.0038023 263
264 69696 18399744 16.24808 6.41507 0.0037879 264
265 70225 18609625 16.27882 6.42316 0.0037736 265
266 70756 18821096 16.30951 6.43123 0.0037594 266
267 71289 19034163 16.34013 6.43928 0.0037453 267
268 71824 19248832 16.37071 6.44731 0.0037313 268
269 72361 19465109 16.40122 6.45531 0.0037175 269
270 72900 19683000 16.43168 6.46330 0.0037037 270
271 73441 19902511 16.46208 6.47127 0.0036900 271
272 73984 20123648 16.49242 6.47922 0.0036765 272
273 74529 20346417 16.52271 6.48715 0.0036630 273
274 75076 20570824 16.55295 6.49507 0.0036496 274
275 75625 20796875 16.58312 6.50296 0.0036364 275
276 76176 21024576 16.61325 6.51083 0.0036232 276

277 76729 21253933 16.64332 6.51868 0.0036101 277
278 77284 21484952 16.67333 6.52652 0.0035971 278
279 77841 21717639 16.70329 6.53434 0.0035842 279
280 78400 21952000 16.73320 6.54213 0.0035714 280
281 78961 22188041 16.76305 6.54991 0.0035587 281
282 79524 22425768 16.79286 6.55767 0.0035461 282
283 80089 22665187 16.82260 6.56541 0.0035336 283
284 80656 22906304 16.85230 6.57314 0.0035211 284
285 81225 23149125 16.88194 6.58084 0.0035088 285
286 81796 23393656 16.91153 6.58853 0.0034965 286
287 82369 23639903 16.94107 6.59620 0.0034843 287
288 82944 23887872 16.97056 6.60385 0.0034722 288
289 83521 24137569 17.00000 6.61149 0.0034602 289
290 84100 24389000 17.02939 6.61911 0.0034483 290
291 84681 24642171 17.05872 6.62671 0.0034364 291
292 85264 24897088 17.08801 6.63429 0.0034247 292
293 85849 25153757 17.11724 6.64185 0.0034130 293
294 86436 25412184 17.14643 6.64940 0.0034014 294
295 87025 25672375 17.17556 6.65693 0.0033898 295
296 87616 25934336 17.20465 6.66444 0.0033784 296
297 88209 26198073 17.23369 6.67194 0.0033670 297
298 88804 26463592 17.26268 6.67942 0.0033557 298
299 89401 26730899 17.29162 6.68688 0.0033445 299
300 90000 27000000 17.32051 6.69433 0.0033333 300
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2850 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 301 to 350
No. Square Cube Sq. Root Cube Root Reciprocal No.
301 90601 27270901 17.34935 6.70176 0.0033223 301

302 91204 27543608 17.37815 6.70917 0.0033113 302
303 91809 27818127 17.40690 6.71657 0.0033003 303
304 92416 28094464 17.43560 6.72395 0.0032895 304
305 93025 28372625 17.46425 6.73132 0.0032787 305
306 93636 28652616 17.49286 6.73866 0.0032680 306
307 94249 28934443 17.52142 6.74600 0.0032573 307
308 94864 29218112 17.54993 6.75331 0.0032468 308
309 95481 29503629 17.57840 6.76061 0.0032362 309
310 96100 29791000 17.60682 6.76790 0.0032258 310
311 96721 30080231 17.63519 6.77517 0.0032154 311
312 97344 30371328 17.66352 6.78242 0.0032051 312
313 97969 30664297 17.69181 6.78966 0.0031949 313
314 98596 30959144 17.72005 6.79688 0.0031847 314
315 99225 31255875 17.74824 6.80409 0.0031746 315
316 99856 31554496 17.77639 6.81128 0.0031646 316
317 100489 31855013 17.80449 6.81846 0.0031546 317
318 101124 32157432 17.83255 6.82562 0.0031447 318
319 101761 32461759 17.86057 6.83277 0.0031348 319
320 102400 32768000 17.88854 6.83990 0.0031250 320
321 103041 33076161 17.91647 6.84702 0.0031153 321
322 103684 33386248 17.94436 6.85412 0.0031056 322
323 104329 33698267 17.97220 6.86121 0.0030960 323
324 104976 34012224 18.00000 6.86829 0.0030864 324
325 105625 34328125 18.02776 6.87534 0.0030769 325
326 106276 34645976 18.05547 6.88239 0.0030675 326
327 106929 34965783 18.08314 6.88942 0.0030581 327
328 107584 35287552 18.11077 6.89643 0.0030488 328
329 108241 35611289 18.13836 6.90344 0.0030395 329
330 108900 35937000 18.16590 6.91042 0.0030303 330
331 109561 36264691 18.19341 6.91740 0.0030211 331

332 110224 36594368 18.22087 6.92436 0.0030120 332
333 110889 36926037 18.24829 6.93130 0.0030030 333
334 111556 37259704 18.27567 6.93823 0.0029940 334
335 112225 37595375 18.30301 6.94515 0.0029851 335
336 112896 37933056 18.33030 6.95205 0.0029762 336
337 113569 38272753 18.35756 6.95894 0.0029674 337
338 114244 38614472 18.38478 6.96582 0.0029586 338
339 114921 38958219 18.41195 6.97268 0.0029499 339
340 115600 39304000 18.43909 6.97953 0.0029412 340
341 116281 39651821 18.46619 6.98637 0.0029326 341
342 116964 40001688 18.49324 6.99319 0.0029240 342
343 117649 40353607 18.52026 7.00000 0.0029155 343
344 118336 40707584 18.54724 7.00680 0.0029070 344
345 119025 41063625 18.57418 7.01358 0.0028986 345
346 119716 41421736 18.60108 7.02035 0.0028902 346
347 120409 41781923 18.62794 7.02711 0.0028818 347
348 121104 42144192 18.65476 7.03385 0.0028736 348
349 121801 42508549 18.68154 7.04058 0.0028653 349
350 122500 42875000 18.70829 7.04730 0.0028571 350
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2851
Powers, Roots, and Reciprocals From 351 to 400
No. Square Cube Sq. Root Cube Root Reciprocal No.
351 123201 43243551 18.73499 7.05400 0.0028490 351
352 123904 43614208 18.76166 7.06070 0.0028409 352
353 124609 43986977 18.78829 7.06738 0.0028329 353
354 125316 44361864 18.81489 7.07404 0.0028249 354
355 126025 44738875 18.84144 7.08070 0.0028169 355
356 126736 45118016 18.86796 7.08734 0.0028090 356

357 127449 45499293 18.89444 7.09397 0.0028011 357
358 128164 45882712 18.92089 7.10059 0.0027933 358
359 128881 46268279 18.94730 7.10719 0.0027855 359
360 129600 46656000 18.97367 7.11379 0.0027778 360
361 130321 47045881 19.00000 7.12037 0.0027701 361
362 131044 47437928 19.02630 7.12694 0.0027624 362
363 131769 47832147 19.05256 7.13349 0.0027548 363
364 132496 48228544 19.07878 7.14004 0.0027473 364
365 133225 48627125 19.10497 7.14657 0.0027397 365
366 133956 49027896 19.13113 7.15309 0.0027322 366
367 134689 49430863 19.15724 7.15960 0.0027248 367
368 135424 49836032 19.18333 7.16610 0.0027174 368
369 136161 50243409 19.20937 7.17258 0.0027100 369
370 136900 50653000 19.23538 7.17905 0.0027027 370
371 137641 51064811 19.26136 7.18552 0.0026954 371
372 138384 51478848 19.28730 7.19197 0.0026882 372
373 139129 51895117 19.31321 7.19840 0.0026810 373
374 139876 52313624 19.33908 7.20483 0.0026738 374
375 140625 52734375 19.36492 7.21125 0.0026667 375
376 141376 53157376 19.39072 7.21765 0.0026596 376
377 142129 53582633 19.41649 7.22405 0.0026525 377
378 142884 54010152 19.44222 7.23043 0.0026455 378
379 143641 54439939 19.46792 7.23680 0.0026385 379
380 144400 54872000 19.49359 7.24316 0.0026316 380
381 145161 55306341 19.51922 7.24950 0.0026247 381
382 145924 55742968 19.54482 7.25584 0.0026178 382
383 146689 56181887 19.57039 7.26217 0.0026110 383
384 147456 56623104 19.59592 7.26848 0.0026042 384
385 148225 57066625 19.62142 7.27479 0.0025974 385
386 148996 57512456 19.64688 7.28108 0.0025907 386

387 149769 57960603 19.67232 7.28736 0.0025840 387
388 150544 58411072 19.69772 7.29363 0.0025773 388
389 151321 58863869 19.72308 7.29989 0.0025707 389
390 152100 59319000 19.74842 7.30614 0.0025641 390
391 152881 59776471 19.77372 7.31238 0.0025575 391
392 153664 60236288 19.79899 7.31861 0.0025510 392
393 154449 60698457 19.82423 7.32483 0.0025445 393
394 155236 61162984 19.84943 7.33104 0.0025381 394
395 156025 61629875 19.87461 7.33723 0.0025316 395
396 156816 62099136 19.89975 7.34342 0.0025253 396
397 157609 62570773 19.92486 7.34960 0.0025189 397
398 158404 63044792 19.94994 7.35576 0.0025126 398
399 159201 63521199 19.97498 7.36192 0.0025063 399
400 160000 64000000 20.00000 7.36806 0.0025000 400
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2852 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 401 to 450
No. Square Cube Sq. Root Cube Root Reciprocal No.
401 160801 64481201 20.02498 7.37420 0.0024938 401
402 161604 64964808 20.04994 7.38032 0.0024876 402
403 162409 65450827 20.07486 7.38644 0.0024814 403
404 163216 65939264 20.09975 7.39254 0.0024752 404
405 164025 66430125 20.12461 7.39864 0.0024691 405
406 164836 66923416 20.14944 7.40472 0.0024631 406
407 165649 67419143 20.17424 7.41080 0.0024570 407
408 166464 67917312 20.19901 7.41686 0.0024510 408
409 167281 68417929 20.22375 7.42291 0.0024450 409
410 168100 68921000 20.24846 7.42896 0.0024390 410
411 168921 69426531 20.27313 7.43499 0.0024331 411

412 169744 69934528 20.29778 7.44102 0.0024272 412
413 170569 70444997 20.32240 7.44703 0.0024213 413
414 171396 70957944 20.34699 7.45304 0.0024155 414
415 172225 71473375 20.37155 7.45904 0.0024096 415
416 173056 71991296 20.39608 7.46502 0.0024038 416
417 173889 72511713 20.42058 7.47100 0.0023981 417
418 174724 73034632 20.44505 7.47697 0.0023923 418
419 175561 73560059 20.46949 7.48292 0.0023866 419
420 176400 74088000 20.49390 7.48887 0.0023810 420
421 177241 74618461 20.51828 7.49481 0.0023753 421
422 178084 75151448 20.54264 7.50074 0.0023697 422
423 178929 75686967 20.56696 7.50666 0.0023641 423
424 179776 76225024 20.59126 7.51257 0.0023585 424
425 180625 76765625 20.61553 7.51847 0.0023529 425
426 181476 77308776 20.63977 7.52437 0.0023474 426
427 182329 77854483 20.66398 7.53025 0.0023419 427
428 183184 78402752 20.68816 7.53612 0.0023364 428
429 184041 78953589 20.71232 7.54199 0.0023310 429
430 184900 79507000 20.73644 7.54784 0.0023256 430
431 185761 80062991 20.76054 7.55369 0.0023202 431
432 186624 80621568 20.78461 7.55953 0.0023148 432
433 187489 81182737 20.80865 7.56535 0.0023095 433
434 188356 81746504 20.83267 7.57117 0.0023041 434
435 189225 82312875 20.85665 7.57698 0.0022989 435
436 190096 82881856 20.88061 7.58279 0.0022936 436
437 190969 83453453 20.90454 7.58858 0.0022883 437
438 191844 84027672 20.92845 7.59436 0.0022831 438
439 192721 84604519 20.95233 7.60014 0.0022779 439
440 193600 85184000 20.97618 7.60590 0.0022727 440
441 194481 85766121 21.00000 7.61166 0.0022676 441

442 195364 86350888 21.02380 7.61741 0.0022624 442
443 196249 86938307 21.04757 7.62315 0.0022573 443
444 197136 87528384 21.07131 7.62888 0.0022523 444
445 198025 88121125 21.09502 7.63461 0.0022472 445
446 198916 88716536 21.11871 7.64032 0.0022422 446
447 199809 89314623 21.14237 7.64603 0.0022371 447
448 200704 89915392 21.16601 7.65172 0.0022321 448
449 201601 90518849 21.18962 7.65741 0.0022272 449
450 202500 91125000 21.21320 7.66309 0.0022222 450
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2853
Powers, Roots, and Reciprocals From 451 to 500
No. Square Cube Sq. Root Cube Root Reciprocal No.
451 203401 91733851 21.23676 7.66877 0.0022173 451
452 204304 92345408 21.26029 7.67443 0.0022124 452
453 205209 92959677 21.28380 7.68009 0.0022075 453
454 206116 93576664 21.30728 7.68573 0.0022026 454
455 207025 94196375 21.33073 7.69137 0.0021978 455
456 207936 94818816 21.35416 7.69700 0.0021930 456
457 208849 95443993 21.37756 7.70262 0.0021882 457
458 209764 96071912 21.40093 7.70824 0.0021834 458
459 210681 96702579 21.42429 7.71384 0.0021786 459
460 211600 97336000 21.44761 7.71944 0.0021739 460
461 212521 97972181 21.47091 7.72503 0.0021692 461
462 213444 98611128 21.49419 7.73061 0.0021645 462
463 214369 99252847 21.51743 7.73619 0.0021598 463
464 215296 99897344 21.54066 7.74175 0.0021552 464
465 216225 100544625 21.56386 7.74731 0.0021505 465
466 217156 101194696 21.58703 7.75286 0.0021459 466

467 218089 101847563 21.61018 7.75840 0.0021413 467
468 219024 102503232 21.63331 7.76394 0.0021368 468
469 219961 103161709 21.65641 7.76946 0.0021322 469
470 220900 103823000 21.67948 7.77498 0.0021277 470
471 221841 104487111 21.70253 7.78049 0.0021231 471
472 222784 105154048 21.72556 7.78599 0.0021186 472
473 223729 105823817 21.74856 7.79149 0.0021142 473
474 224676 106496424 21.77154 7.79697 0.0021097 474
475 225625 107171875 21.79449 7.80245 0.0021053 475
476 226576 107850176 21.81742 7.80793 0.0021008 476
477 227529 108531333 21.84033 7.81339 0.0020964 477
478 228484 109215352 21.86321 7.81885 0.0020921 478
479 229441 109902239 21.88607 7.82429 0.0020877 479
480 230400 110592000 21.90890 7.82974 0.0020833 480
481 231361 111284641 21.93171 7.83517 0.0020790 481
482 232324 111980168 21.95450 7.84059 0.0020747 482
483 233289 112678587 21.97726 7.84601 0.0020704 483
484 234256 113379904 22.00000 7.85142 0.0020661 484
485 235225 114084125 22.02272 7.85683 0.0020619 485
486 236196 114791256 22.04541 7.86222 0.0020576 486
487 237169 115501303 22.06808 7.86761 0.0020534 487
488 238144 116214272 22.09072 7.87299 0.0020492 488
489 239121 116930169 22.11334 7.87837 0.0020450 489
490 240100 117649000 22.13594 7.88374 0.0020408 490
491 241081 118370771 22.15852 7.88909 0.0020367 491
492 242064 119095488 22.18107 7.89445 0.0020325 492
493 243049 119823157 22.20360 7.89979 0.0020284 493
494 244036 120553784 22.22611 7.90513 0.0020243 494
495 245025 121287375 22.24860 7.91046 0.0020202 495
496 246016 122023936 22.27106 7.91578 0.0020161 496

497 247009 122763473 22.29350 7.92110 0.0020121 497
498 248004 123505992 22.31591 7.92641 0.0020080 498
499 249001 124251499 22.33831 7.93171 0.0020040 499
500 250000 125000000 22.36068 7.93701 0.0020000 500
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2854 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 501 to 550
No. Square Cube Sq. Root Cube Root Reciprocal No.
501 251001 125751501 22.38303 7.94229 0.0019960 501
502 252004 126506008 22.40536 7.94757 0.0019920 502
503 253009 127263527 22.42766 7.95285 0.0019881 503
504 254016 128024064 22.44994 7.95811 0.0019841 504
505 255025 128787625 22.47221 7.96337 0.0019802 505
506 256036 129554216 22.49444 7.96863 0.0019763 506
507 257049 130323843 22.51666 7.97387 0.0019724 507
508 258064 131096512 22.53886 7.97911 0.0019685 508
509 259081 131872229 22.56103 7.98434 0.0019646 509
510 260100 132651000 22.58318 7.98957 0.0019608 510
511 261121 133432831 22.60531 7.99479 0.0019569 511
512 262144 134217728 22.62742 8.00000 0.0019531 512
513 263169 135005697 22.64950 8.00520 0.0019493 513
514 264196 135796744 22.67157 8.01040 0.0019455 514
515 265225 136590875 22.69361 8.01559 0.0019417 515
516 266256 137388096 22.71563 8.02078 0.0019380 516
517 267289 138188413 22.73763 8.02596 0.0019342 517
518 268324 138991832 22.75961 8.03113 0.0019305 518
519 269361 139798359 22.78157 8.03629 0.0019268 519
520 270400 140608000 22.80351 8.04145 0.0019231 520
521 271441 141420761 22.82542 8.04660 0.0019194 521

522 272484 142236648 22.84732 8.05175 0.0019157 522
523 273529 143055667 22.86919 8.05689 0.0019120 523
524 274576 143877824 22.89105 8.06202 0.0019084 524
525 275625 144703125 22.91288 8.06714 0.0019048 525
526 276676 145531576 22.93469 8.07226 0.0019011 526
527 277729 146363183 22.95648 8.07737 0.0018975 527
528 278784 147197952 22.97825 8.08248 0.0018939 528
529 279841 148035889 23.00000 8.08758 0.0018904 529
530 280900 148877000 23.02173 8.09267 0.0018868 530
531 281961 149721291 23.04344 8.09776 0.0018832 531
532 283024 150568768 23.06513 8.10284 0.0018797 532
533 284089 151419437 23.08679 8.10791 0.0018762 533
534 285156 152273304 23.10844 8.11298 0.0018727 534
535 286225 153130375 23.13007 8.11804 0.0018692 535
536 287296 153990656 23.15167 8.12310 0.0018657 536
537 288369 154854153 23.17326 8.12814 0.0018622 537
538 289444 155720872 23.19483 8.13319 0.0018587 538
539 290521 156590819 23.21637 8.13822 0.0018553 539
540 291600 157464000 23.23790 8.14325 0.0018519 540
541 292681 158340421 23.25941 8.14828 0.0018484 541
542 293764 159220088 23.28089 8.15329 0.0018450 542
543 294849 160103007 23.30236 8.15831 0.0018416 543
544 295936 160989184 23.32381 8.16331 0.0018382 544
545 297025 161878625 23.34524 8.16831 0.0018349 545
546 298116 162771336 23.36664 8.17330 0.0018315 546
547 299209 163667323 23.38803 8.17829 0.0018282 547
548 300304 164566592 23.40940 8.18327 0.0018248 548
549 301401 165469149 23.43075 8.18824 0.0018215 549
550 302500 166375000 23.45208 8.19321 0.0018182 550
Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2855
Powers, Roots, and Reciprocals From 551 to 600
No. Square Cube Sq. Root Cube Root Reciprocal No.
551 303601 167284151 23.47339 8.19818 0.0018149 551
552 304704 168196608 23.49468 8.20313 0.0018116 552
553 305809 169112377 23.51595 8.20808 0.0018083 553
554 306916 170031464 23.53720 8.21303 0.0018051 554
555 308025 170953875 23.55844 8.21797 0.0018018 555
556 309136 171879616 23.57965 8.22290 0.0017986 556
557 310249 172808693 23.60085 8.22783 0.0017953 557
558 311364 173741112 23.62202 8.23275 0.0017921 558
559 312481 174676879 23.64318 8.23766 0.0017889 559
560 313600 175616000 23.66432 8.24257 0.0017857 560
561 314721 176558481 23.68544 8.24747 0.0017825 561
562 315844 177504328 23.70654 8.25237 0.0017794 562
563 316969 178453547 23.72762 8.25726 0.0017762 563
564 318096 179406144 23.74868 8.26215 0.0017730 564
565 319225 180362125 23.76973 8.26703 0.0017699 565
566 320356 181321496 23.79075 8.27190 0.0017668 566
567 321489 182284263 23.81176 8.27677 0.0017637 567
568 322624 183250432 23.83275 8.28164 0.0017606 568
569 323761 184220009 23.85372 8.28649 0.0017575 569
570 324900 185193000 23.87467 8.29134 0.0017544 570
571 326041 186169411 23.89561 8.29619 0.0017513 571
572 327184 187149248 23.91652 8.30103 0.0017483 572
573 328329 188132517 23.93742 8.30587 0.0017452 573
574 329476 189119224 23.95830 8.31069 0.0017422 574
575 330625 190109375 23.97916 8.31552 0.0017391 575
576 331776 191102976 24.00000 8.32034 0.0017361 576

577 332929 192100033 24.02082 8.32515 0.0017331 577
578 334084 193100552 24.04163 8.32995 0.0017301 578
579 335241 194104539 24.06242 8.33476 0.0017271 579
580 336400 195112000 24.08319 8.33955 0.0017241 580
581 337561 196122941 24.10394 8.34434 0.0017212 581
582 338724 197137368 24.12468 8.34913 0.0017182 582
583 339889 198155287 24.14539 8.35390 0.0017153 583
584 341056 199176704 24.16609 8.35868 0.0017123 584
585 342225 200201625 24.18677 8.36345 0.0017094 585
586 343396 201230056 24.20744 8.36821 0.0017065 586
587 344569 202262003 24.22808 8.37297 0.0017036 587
588 345744 203297472 24.24871 8.37772 0.0017007 588
589 346921 204336469 24.26932 8.38247 0.0016978 589
590 348100 205379000 24.28992 8.38721 0.0016949 590
591 349281 206425071 24.31049 8.39194 0.0016920 591
592 350464 207474688 24.33105 8.39667 0.0016892 592
593 351649 208527857 24.35159 8.40140 0.0016863 593
594 352836 209584584 24.37212 8.40612 0.0016835 594
595 354025 210644875 24.39262 8.41083 0.0016807 595
596 355216 211708736 24.41311 8.41554 0.0016779 596
597 356409 212776173 24.43358 8.42025 0.0016750 597
598 357604 213847192 24.45404 8.42494 0.0016722 598
599 358801 214921799 24.47448 8.42964 0.0016694 599
600 360000 216000000 24.49490 8.43433 0.0016667 600
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2856 POWERS, ROOTS, AND RECIPROCALS
Powers, Roots, and Reciprocals From 601 to 650
No. Square Cube Sq. Root Cube Root Reciprocal No.
601 361201 217081801 24.51530 8.43901 0.0016639 601

602 362404 218167208 24.53569 8.44369 0.0016611 602
603 363609 219256227 24.55606 8.44836 0.0016584 603
604 364816 220348864 24.57641 8.45303 0.0016556 604
605 366025 221445125 24.59675 8.45769 0.0016529 605
606 367236 222545016 24.61707 8.46235 0.0016502 606
607 368449 223648543 24.63737 8.46700 0.0016474 607
608 369664 224755712 24.65766 8.47165 0.0016447 608
609 370881 225866529 24.67793 8.47629 0.0016420 609
610 372100 226981000 24.69818 8.48093 0.0016393 610
611 373321 228099131 24.71841 8.48556 0.0016367 611
612 374544 229220928 24.73863 8.49018 0.0016340 612
613 375769 230346397 24.75884 8.49481 0.0016313 613
614 376996 231475544 24.77902 8.49942 0.0016287 614
615 378225 232608375 24.79919 8.50403 0.0016260 615
616 379456 233744896 24.81935 8.50864 0.0016234 616
617 380689 234885113 24.83948 8.51324 0.0016207 617
618 381924 236029032 24.85961 8.51784 0.0016181 618
619 383161 237176659 24.87971 8.52243 0.0016155 619
620 384400 238328000 24.89980 8.52702 0.0016129 620
621 385641 239483061 24.91987 8.53160 0.0016103 621
622 386884 240641848 24.93993 8.53618 0.0016077 622
623 388129 241804367 24.95997 8.54075 0.0016051 623
624 389376 242970624 24.97999 8.54532 0.0016026 624
625 390625 244140625 25.00000 8.54988 0.0016000 625
626 391876 245314376 25.01999 8.55444 0.0015974 626
627 393129 246491883 25.03997 8.55899 0.0015949 627
628 394384 247673152 25.05993 8.56354 0.0015924 628
629 395641 248858189 25.07987 8.56808 0.0015898 629
630 396900 250047000 25.09980 8.57262 0.0015873 630
631 398161 251239591 25.11971 8.57715 0.0015848 631

632 399424 252435968 25.13961 8.58168 0.0015823 632
633 400689 253636137 25.15949 8.58620 0.0015798 633
634 401956 254840104 25.17936 8.59072 0.0015773 634
635 403225 256047875 25.19921 8.59524 0.0015748 635
636 404496 257259456 25.21904 8.59975 0.0015723 636
637 405769 258474853 25.23886 8.60425 0.0015699 637
638 407044 259694072 25.25866 8.60875 0.0015674 638
639 408321 260917119 25.27845 8.61325 0.0015649 639
640 409600 262144000 25.29822 8.61774 0.0015625 640
641 410881 263374721 25.31798 8.62222 0.0015601 641
642 412164 264609288 25.33772 8.62671 0.0015576 642
643 413449 265847707 25.35744 8.63118 0.0015552 643
644 414736 267089984 25.37716 8.63566 0.0015528 644
645 416025 268336125 25.39685 8.64012 0.0015504 645
646 417316 269586136 25.41653 8.64459 0.0015480 646
647 418609 270840023 25.43619 8.64904 0.0015456 647
648 419904 272097792 25.45584 8.65350 0.0015432 648
649 421201 273359449 25.47548 8.65795 0.0015408 649
650 422500 274625000 25.49510 8.66239 0.0015385 650
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWERS, ROOTS, AND RECIPROCALS 2857
Powers, Roots, and Reciprocals From 651 to 700
No. Square Cube Sq. Root Cube Root Reciprocal No.
651 423801 275894451 25.51470 8.66683 0.0015361 651
652 425104 277167808 25.53429 8.67127 0.0015337 652
653 426409 278445077 25.55386 8.67570 0.0015314 653
654 427716 279726264 25.57342 8.68012 0.0015291 654
655 429025 281011375 25.59297 8.68455 0.0015267 655
656 430336 282300416 25.61250 8.68896 0.0015244 656

657 431649 283593393 25.63201 8.69338 0.0015221 657
658 432964 284890312 25.65151 8.69778 0.0015198 658
659 434281 286191179 25.67100 8.70219 0.0015175 659
660 435600 287496000 25.69047 8.70659 0.0015152 660
661 436921 288804781 25.70992 8.71098 0.0015129 661
662 438244 290117528 25.72936 8.71537 0.0015106 662
663 439569 291434247 25.74879 8.71976 0.0015083 663
664 440896 292754944 25.76820 8.72414 0.0015060 664
665 442225 294079625 25.78759 8.72852 0.0015038 665
666 443556 295408296 25.80698 8.73289 0.0015015 666
667 444889 296740963 25.82634 8.73726 0.0014993 667
668 446224 298077632 25.84570 8.74162 0.0014970 668
669 447561 299418309 25.86503 8.74598 0.0014948 669
670 448900 300763000 25.88436 8.75034 0.0014925 670
671 450241 302111711 25.90367 8.75469 0.0014903 671
672 451584 303464448 25.92296 8.75904 0.0014881 672
673 452929 304821217 25.94224 8.76338 0.0014859 673
674 454276 306182024 25.96151 8.76772 0.0014837 674
675 455625 307546875 25.98076 8.77205 0.0014815 675
676 456976 308915776 26.00000 8.77638 0.0014793 676
677 458329 310288733 26.01922 8.78071 0.0014771 677
678 459684 311665752 26.03843 8.78503 0.0014749 678
679 461041 313046839 26.05763 8.78935 0.0014728 679
680 462400 314432000 26.07681 8.79366 0.0014706 680
681 463761 315821241 26.09598 8.79797 0.0014684 681
682 465124 317214568 26.11513 8.80227 0.0014663 682
683 466489 318611987 26.13427 8.80657 0.0014641 683
684 467856 320013504 26.15339 8.81087 0.0014620 684
685 469225 321419125 26.17250 8.81516 0.0014599 685
686 470596 322828856 26.19160 8.81945 0.0014577 686

687 471969 324242703 26.21068 8.82373 0.0014556 687
688 473344 325660672 26.22975 8.82801 0.0014535 688
689 474721 327082769 26.24881 8.83228 0.0014514 689
690 476100 328509000 26.26785 8.83656 0.0014493 690
691 477481 329939371 26.28688 8.84082 0.0014472 691
692 478864 331373888 26.30589 8.84509 0.0014451 692
693 480249 332812557 26.32489 8.84934 0.0014430 693
694 481636 334255384 26.34388 8.85360 0.0014409 694
695 483025 335702375 26.36285 8.85785 0.0014388 695
696 484416 337153536 26.38181 8.86210 0.0014368 696
697 485809 338608873 26.40076 8.86634 0.0014347 697
698 487204 340068392 26.41969 8.87058 0.0014327 698
699 488601 341532099 26.43861 8.87481 0.0014306 699
700 490000 343000000 26.45751 8.87904 0.0014286 700
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY